diff --git a/docs/js-udf.md b/docs/js-udf.md
index cff2a852..52861b08 100644
--- a/docs/js-udf.md
+++ b/docs/js-udf.md
@@ -143,6 +143,11 @@ Let's take an example of a function to get the second maximum values from the gr
 | 5     | deserialize(str) | No        | Opposite to serialize(). Read the string and convert back to JS internal state. | function(str)\{<br />let s=JSON.parse(str);<br />this.max=s['max'];<br />this.sec_max=s['sec_max'];<br />} |
 | 6     | merge(str)       | No        | Merges two states into one. Used for multiple shards processing. | function(str)\{<br />let s=JSON.parse(str);<br />if..else..}  |
 
+**Emit strategy and return shape**
+
+- Default (no `has_customized_emit`): `finalize()` must return a single value matching the declared return type. Any value returned from `process()` is ignored.
+- Custom emit (`has_customized_emit: true`): `process()` should return an integer (or `true`/`false`) indicating how many results to emit now, and `finalize()` must return an array whose length equals that emit count.
+
 
 
 ### Example: get second largest number {#udaf-example}
diff --git a/docs/py-udf.md b/docs/py-udf.md
index e0843580..4517af7a 100644
--- a/docs/py-udf.md
+++ b/docs/py-udf.md
@@ -99,6 +99,12 @@ The function list:
 * `deserialize` load the state from checkpoint to the internal state, optional.
 * `merge` for multi-shard processing, merge the states from each shard, optional.
 
+**Emit strategy and return shape**
+
+- By default, Proton calls `finalize()` once and expects a *single* value of the declared return type (not a list). Any value returned from `process()` is ignored in this mode.
+- If you need to emit multiple results per group, set `self.has_customized_emit = True` in `__init__`, return either an integer count or `True`/`False` from `process()` to indicate how many results to emit, and return a list from `finalize()` whose length matches that count.
+- Only one UDA with `has_customized_emit = True` is supported per streaming query.
+
 ## Examples
 
 ### A simple UDF without dependency
@@ -166,7 +172,7 @@ class getMax:
             if item > self.max:
                 self.max = item
     def finalize(self):
-        return [self.max]
+        return self.max
 $$;
 ```