When did Babylon capture Assyria?

Assyria was gradually erased from the map starting with the Battle of Ninevah in 612BC, and concluding with the defeat of the Egyptian/Assyrian armies at the Battle of Carchemish in 605BC. For reasons best known to himself, the Judean King Josiah tried to intercept the Egyptian army on its way to Carchemish, and was killed for his trouble.

Exercise caution - ancient dates are always controversial

http://www.scaruffi.com/politics/neareast.html

626 BC: the Medes/Persians defeat the Scythians

625 BC: Median king Cyaxares moves the capital to Ecbatana (Hamadan)

625 BC: Chaldean chief Nabopolassar seized power in Babylon

615 BC: the Medes capture Assyrian cities

616 BC: Chaldean king Nabopolassar captures Babylon

612 BC: the Babylonians, led by king Nabopolassar, and their allies the Medes, led by Cyaxares, destroy the Assyrian capital of Nineveh (as well as Nimrud) and split the Assyrian empire (Mesopotamia to Babylon and Elam to Media) while Egypt recovers control of Palestine and Syria