You asked:
What happens in case an instance of the Browser activity (for example) already exists in the same task (stack) of my app's activity (but not in the foreground) ? How is it brought forward? This is not described in the doc.
It is not possible for an instance of the Browser activity (to use your example) to exist in your app's task stack, because that Activity
has been defined with singleTask
launch mode and has a different taskAffinity
from the other activities in your app. Therefore, whenever the Browser activity is launched, it will always be launched into its own task, and not into your task.