Puranas, Genesis, Epic of Gilgamesh, Deucalion all contain flood myths in a reasonably close area. But the Mayans and Australians also had their own share of flood myths? Which is more possible?
I wont answer as a historian, but as a geologist: floods leave recognisable deposits, which are relatively straightforward to date precisely. There is no single widespread flood event deposit associated with the reported events throughout the enumerated areas, which form a quite discontinuous area.
I would go with multiple small local floods, inasmuch as each is actually rooted in a historical event.
fyi, you'll find more on this in the FAQ