diff --git a/docs/batch-client-reference.md b/docs/batch-client-reference.md
index c2a4c92..875b3cb 100644
--- a/docs/batch-client-reference.md
+++ b/docs/batch-client-reference.md
@@ -108,7 +108,7 @@ for anyway.
 def submit_regular(urls: list[str | TaskInputDict] | None = None,
                    *,
                    file_input_id: str | None = None,
-                   zenrows_params: dict[str, str] | None = None,
+                   zenrows_params: ParamMap | None = None,
                    external_id: str | None = None,
                    name: str | None = None,
                    metadata: dict[str, str] | None = None,
@@ -140,7 +140,7 @@ open-and-extend pattern see `submit_open`.
 ```python
 def submit_open(urls: list[str | TaskInputDict] | None = None,
                 *,
-                zenrows_params: dict[str, str] | None = None,
+                zenrows_params: ParamMap | None = None,
                 external_id: str | None = None,
                 name: str | None = None,
                 metadata: dict[str, str] | None = None,
@@ -169,7 +169,7 @@ def submit_scheduled(schedule: Schedule | JobScheduleDict,
                      urls: list[str | TaskInputDict] | None = None,
                      *,
                      file_input_id: str | None = None,
-                     zenrows_params: dict[str, str] | None = None,
+                     zenrows_params: ParamMap | None = None,
                      external_id: str | None = None,
                      name: str | None = None,
                      metadata: dict[str, str] | None = None,
@@ -1597,6 +1597,12 @@ exactly one tier. If a malformed param map carries both, `auto`
 wins here (it's what the engine would honor) — but the server would
 reject that body at submit anyway.
 
+<a id="ParamValue"></a>
+
+#### ParamValue
+
+dict form: `custom_headers` map
+
 <a id="Tier"></a>
 
 ## Tier Objects
@@ -2132,12 +2138,13 @@ rows). Flip via `POST /jobs/{id}/pause` and
 class IngestStatus(Enum)
 ```
 
-Present only on runs created by a large (202) submission.
-`pending` — task rows are still streaming into storage;
-reads may return partial pages and `addTasks` returns
-`409`. `done` — every accepted task row is visible.
-Omitted on runs whose tasks were written on the request
-path (201 submissions, `addTasks` batches, reruns).
+Present only on runs created by a large (202) submission
+or a large (202) rerun. `pending` — task rows are still
+streaming into storage; reads may return partial pages
+and `addTasks` returns `409`. `done` — every accepted
+task row is visible. Omitted on runs whose tasks were
+written on the request path (201 submissions and
+reruns, `addTasks` batches).
 
 <a id="FailureReason"></a>
 
@@ -2182,12 +2189,13 @@ rows). Flip via `POST /jobs/{id}/pause` and
 
 #### ingest\_status
 
-Present only on runs created by a large (202) submission.
-`pending` — task rows are still streaming into storage;
-reads may return partial pages and `addTasks` returns
-`409`. `done` — every accepted task row is visible.
-Omitted on runs whose tasks were written on the request
-path (201 submissions, `addTasks` batches, reruns).
+Present only on runs created by a large (202) submission
+or a large (202) rerun. `pending` — task rows are still
+streaming into storage; reads may return partial pages
+and `addTasks` returns `409`. `done` — every accepted
+task row is visible. Omitted on runs whose tasks were
+written on the request path (201 submissions and
+reruns, `addTasks` batches).
 
 <a id="Run.failure_reason"></a>
 
@@ -2737,7 +2745,7 @@ Omitted when the caller did not supply one.
 
 #### result\_url
 
-2-hour presigned download URL for the result body, or a
+24-hour presigned download URL for the result body, or a
 `/v1/jobs/<id>/runs/<run>/tasks/<tid>/content` URL you can
 fetch directly. Empty for non-successful tasks.
 
diff --git a/docs/openapi.yaml b/docs/openapi.yaml
index 8acb757..e467732 100644
--- a/docs/openapi.yaml
+++ b/docs/openapi.yaml
@@ -422,6 +422,12 @@ paths:
         - Auto-closes an `open` job (existing behavior).
         - Honors `Idempotency-Key`: a repeat call with the same
           key returns the original new-run id.
+
+        Large reruns are accepted asynchronously: past a server-side
+        row-count threshold (the same one that upgrades large
+        submissions) the call returns `202` and the new run's task
+        rows stream into storage off the request path. Treat `201`
+        and `202` both as success.
       parameters:
         - in: query
           name: status
@@ -437,7 +443,20 @@ paths:
         - $ref: '#/components/parameters/IdempotencyKey'
       responses:
         '201':
-          description: New run created.
+          description: New run created (sync path). All task rows are written.
+          content:
+            application/json:
+              schema: { $ref: '#/components/schemas/RerunJobResponse' }
+        '202':
+          description: |
+            New run accepted (large rerun). `retried_tasks` /
+            `inherited_tasks` are the final counts, but individual
+            task rows stream into storage off the request path.
+            `latest_run.ingest_status` is `pending` in this response
+            and flips to `done` on `GET /v1/jobs/{id}` once every
+            task row is visible; the run's `stats.total` is correct
+            from this response forward, so completion polling is
+            safe. Body shape matches the 201 response.
           content:
             application/json:
               schema: { $ref: '#/components/schemas/RerunJobResponse' }
@@ -1246,11 +1265,24 @@ components:
         `session_id`, `original_status`, `allowed_status_codes`,
         `wait_for`, `wait`, `block_resources`, `json_response`,
         `css_extractor`, `autoparse`, `response_type`, `outputs`.
+
+        `custom_headers` additionally accepts an object of header
+        name → value pairs (or that object serialised as a JSON
+        string), e.g. `{"custom_headers": {"Referer":
+        "https://www.google.com/"}}`. The headers are forwarded to
+        the scraping target, subject to the scraper API's usual
+        header sanitisation. At most 32 headers / 8 KB serialised;
+        names must be valid HTTP tokens. Header filtering and
+        browser-header sanitisation are owned by the scraper API,
+        not Conveyor. A task-level
+        `custom_headers` replaces the job-level object wholesale —
+        no per-name merging.
       additionalProperties:
         oneOf:
           - { type: string }
           - { type: boolean }
           - { type: integer }
+          - { type: object, additionalProperties: { type: string } }
 
     TaskInput:
       type: object
@@ -1509,12 +1541,13 @@ components:
           type: string
           enum: [pending, done]
           description: |
-            Present only on runs created by a large (202) submission.
-            `pending` — task rows are still streaming into storage;
-            reads may return partial pages and `addTasks` returns
-            `409`. `done` — every accepted task row is visible.
-            Omitted on runs whose tasks were written on the request
-            path (201 submissions, `addTasks` batches, reruns).
+            Present only on runs created by a large (202) submission
+            or a large (202) rerun. `pending` — task rows are still
+            streaming into storage; reads may return partial pages
+            and `addTasks` returns `409`. `done` — every accepted
+            task row is visible. Omitted on runs whose tasks were
+            written on the request path (201 submissions and
+            reruns, `addTasks` batches).
         created_at: { type: string, format: date-time }
         updated_at: { type: string, format: date-time }
         failure_reason:
@@ -1731,7 +1764,7 @@ components:
           type: string
           nullable: true
           description: |
-            2-hour presigned download URL for the result body, or a
+            24-hour presigned download URL for the result body, or a
             `/v1/jobs/<id>/runs/<run>/tasks/<tid>/content` URL you can
             fetch directly. Empty for non-successful tasks.
         error:
diff --git a/src/zenrows/batch/_estimate.py b/src/zenrows/batch/_estimate.py
index 01e5be2..f730ab6 100644
--- a/src/zenrows/batch/_estimate.py
+++ b/src/zenrows/batch/_estimate.py
@@ -50,7 +50,7 @@
 _TRUTHY = frozenset({"true", "1", "yes", "on"})
 
 # What `Tier` keys can appear, in the order a breakdown should render.
-ParamValue = str | bool | int
+ParamValue = str | bool | int | dict[str, str]  # dict form: `custom_headers` map
 ParamMap = dict[str, ParamValue]
 TaskLike = str | TaskInput | dict
 
diff --git a/src/zenrows/batch/client.py b/src/zenrows/batch/client.py
index 1855af1..dc5ea3a 100644
--- a/src/zenrows/batch/client.py
+++ b/src/zenrows/batch/client.py
@@ -46,7 +46,7 @@
     download_to_dir,
     download_to_memory,
 )
-from zenrows.batch._estimate import CostEstimate, _estimate_cost
+from zenrows.batch._estimate import CostEstimate, ParamMap, _estimate_cost
 from zenrows.batch._resources import (
     ExportHandle,
     ExportRef,
@@ -236,7 +236,7 @@ def submit_regular(
         urls: list[str | TaskInputDict] | None = None,
         *,
         file_input_id: str | None = None,
-        zenrows_params: dict[str, str] | None = None,
+        zenrows_params: ParamMap | None = None,
         external_id: str | None = None,
         name: str | None = None,
         metadata: dict[str, str] | None = None,
@@ -279,7 +279,7 @@ def submit_open(
         self,
         urls: list[str | TaskInputDict] | None = None,
         *,
-        zenrows_params: dict[str, str] | None = None,
+        zenrows_params: ParamMap | None = None,
         external_id: str | None = None,
         name: str | None = None,
         metadata: dict[str, str] | None = None,
@@ -319,7 +319,7 @@ def submit_scheduled(
         urls: list[str | TaskInputDict] | None = None,
         *,
         file_input_id: str | None = None,
-        zenrows_params: dict[str, str] | None = None,
+        zenrows_params: ParamMap | None = None,
         external_id: str | None = None,
         name: str | None = None,
         metadata: dict[str, str] | None = None,
@@ -1156,7 +1156,7 @@ def _build_submit_body(
     urls: list[str | TaskInputDict] | None,
     file_input_id: str | None,
     status: Literal["open", "closed"],
-    zenrows_params: dict[str, str] | None,
+    zenrows_params: ParamMap | None,
     schedule: JobScheduleDict | None = None,
     external_id: str | None = None,
     name: str | None = None,
diff --git a/src/zenrows/batch/models.py b/src/zenrows/batch/models.py
index 75e924b..90361c0 100644
--- a/src/zenrows/batch/models.py
+++ b/src/zenrows/batch/models.py
@@ -1,6 +1,6 @@
 # generated by datamodel-codegen:
 #   filename:  openapi.yaml
-#   timestamp: 2026-07-08T16:45:00+00:00
+#   timestamp: 2026-07-21T11:46:07+00:00
 
 from __future__ import annotations
 
@@ -164,7 +164,7 @@ class TaskInput(BaseModel):
     Must be http(s). Other schemes rejected at submit.
     """
     metadata: Annotated[dict[str, str] | None, Field(max_length=20)] = None
-    zenrows_params: dict[str, str | bool | int] | None = None
+    zenrows_params: dict[str, str | bool | int | dict[str, str]] | None = None
     """
     Per-task scraper params. Override the job-level
     `zenrows_params` on key collision (task wins).
@@ -276,12 +276,13 @@ class PauseState(Enum):
 
 class IngestStatus(Enum):
     """
-    Present only on runs created by a large (202) submission.
-    `pending` — task rows are still streaming into storage;
-    reads may return partial pages and `addTasks` returns
-    `409`. `done` — every accepted task row is visible.
-    Omitted on runs whose tasks were written on the request
-    path (201 submissions, `addTasks` batches, reruns).
+    Present only on runs created by a large (202) submission
+    or a large (202) rerun. `pending` — task rows are still
+    streaming into storage; reads may return partial pages
+    and `addTasks` returns `409`. `done` — every accepted
+    task row is visible. Omitted on runs whose tasks were
+    written on the request path (201 submissions and
+    reruns, `addTasks` batches).
 
     """
 
@@ -326,12 +327,13 @@ class Run(BaseModel):
     """
     ingest_status: IngestStatus | None = None
     """
-    Present only on runs created by a large (202) submission.
-    `pending` — task rows are still streaming into storage;
-    reads may return partial pages and `addTasks` returns
-    `409`. `done` — every accepted task row is visible.
-    Omitted on runs whose tasks were written on the request
-    path (201 submissions, `addTasks` batches, reruns).
+    Present only on runs created by a large (202) submission
+    or a large (202) rerun. `pending` — task rows are still
+    streaming into storage; reads may return partial pages
+    and `addTasks` returns `409`. `done` — every accepted
+    task row is visible. Omitted on runs whose tasks were
+    written on the request path (201 submissions and
+    reruns, `addTasks` batches).
 
     """
     created_at: AwareDatetime
@@ -859,7 +861,7 @@ class TaskResult(BaseModel):
     type: ResultType | None = None
     result_url: str | None = None
     """
-    2-hour presigned download URL for the result body, or a
+    24-hour presigned download URL for the result body, or a
     `/v1/jobs/<id>/runs/<run>/tasks/<tid>/content` URL you can
     fetch directly. Empty for non-successful tasks.
 
@@ -1023,7 +1025,7 @@ class SubmitJobRequest(BaseModel):
     is auto-closed.
 
     """
-    zenrows_params: dict[str, str | bool | int] | None = None
+    zenrows_params: dict[str, str | bool | int | dict[str, str]] | None = None
     """
     Job-level scraper params, applied to every task of every
     run of the job. Each task can override individual keys