Repository: pydantic/pydantic

Issue:
Documentation for `_parent_depth` in `TypeAdapter`
### Initial Checks

- [X] I have searched Google & GitHub for similar requests and couldn't find anything
- [X] I have read and followed [the docs](https://docs.pydantic.dev) and still think this feature is missing

### Description

In the [documentation for `TypeAdapter`](https://docs.pydantic.dev/latest/api/type_adapter/#pydantic.type_adapter.TypeAdapter), the `_parent_depth` arg is noted but not explained.

It appears this is related to module namespaces and type hint extraction, but the usage isn't clear.

Can we get documentation for this arg? If it is intended for internal use only, as denoted by its name, it could be described as such, just to reduce potential confusion and footgunning.

### Affected Components

- [ ] [Compatibility between releases](https://docs.pydantic.dev/changelog/)
- [X] [Data validation/parsing](https://docs.pydantic.dev/concepts/models/#basic-model-usage)
- [ ] [Data serialization](https://docs.pydantic.dev/concepts/serialization/) - `.model_dump()` and `.model_dump_json()`
- [ ] [JSON Schema](https://docs.pydantic.dev/concepts/json_schema/)
- [ ] [Dataclasses](https://docs.pydantic.dev/concepts/dataclasses/)
- [ ] [Model Config](https://docs.pydantic.dev/concepts/config/)
- [ ] [Field Types](https://docs.pydantic.dev/api/types/) - adding or changing a particular data type
- [ ] [Function validation decorator](https://docs.pydantic.dev/concepts/validation_decorator/)
- [ ] [Generic Models](https://docs.pydantic.dev/concepts/models/#generic-models)
- [ ] [Other Model behaviour](https://docs.pydantic.dev/concepts/models/) - `model_construct()`, pickling, private attributes, ORM mode
- [ ] [Plugins](https://docs.pydantic.dev/) and integration with other tools - mypy, FastAPI, python-devtools, Hypothesis, VS Code, PyCharm, etc.


Discussion:
Hi @psychedelicious,

Yep, I think a docs update is certainly merited here 👍. I'll work on this update this week.

Resolving patch:
diff --git a/pydantic/type_adapter.py b/pydantic/type_adapter.py
--- a/pydantic/type_adapter.py
+++ b/pydantic/type_adapter.py
@@ -216,7 +216,26 @@ def __init__(self, type: T, *, config: ConfigDict | None = None, _parent_depth:
             ...
 
     def __init__(self, type: Any, *, config: ConfigDict | None = None, _parent_depth: int = 2) -> None:
-        """Initializes the TypeAdapter object."""
+        """Initializes the TypeAdapter object.
+
+        Args:
+            type: The type associated with the `TypeAdapter`.
+            config: Configuration for the `TypeAdapter`, should be a dictionary conforming to [`ConfigDict`][pydantic.config.ConfigDict].
+            _parent_depth: depth at which to search the parent namespace to construct the local namespace.
+
+        !!! note
+            You cannot use the `config` argument when instantiating a `TypeAdapter` if the type you're using has its own
+            config that cannot be overridden (ex: `BaseModel`, `TypedDict`, and `dataclass`). A
+            [`type-adapter-config-unused`](../errors/usage_errors.md#type-adapter-config-unused) error will be raised in this case.
+
+        !!! note
+            The `_parent_depth` argument is named with an underscore to suggest its private nature and discourage use.
+            It may be deprecated in a minor version, so we only recommend using it if you're
+            comfortable with potential change in behavior / support.
+
+        Returns:
+            A type adapter configured for the specified `type`.
+        """
         config_wrapper = _config.ConfigWrapper(config)
 
         try:


Test patch: