Question: The documentation says it should be used instead of LocalStorage, but it doesn't list anything regarding how large it is. If I recall, LocalStorage in web browsers is only about 10mb.

<https://facebook.github.io/react-native/docs/asyncstorage.html>

Answer: 
It writes to disk and is very large if there is free space. On iOS there are no artificial caps other than what the underlying operating system imposes: <https://stackoverflow.com/a/1897383/454967>.
The new way of increasing AsyncStorage size on react-native is to add `AsyncStorage_db_size_in_MB=` property to your `android/gradle.properties` as shown here: <https://react-native-async-storage.github.io/async-storage/docs/advanced/db_size/>