>But if you are going to say that - why describe it as a “split”, as opposed to two separate universes which happen to identical in contents up to some point, non-identical thereafter?

But they are (presumed under this model to be) splitting. You posited a case where two later happen to be identical, but that doesn't mean they merge. You'd just have two of them.

>Also, what you say about dollars is true because they have certain properties - effectively they have two different criteria of identity, one economic, the other physical. What is the criterion of identity for universes/branches?

I'd guess that there is none, like electrons. But though those are even more indistinguishable than dollars, you can still have two of them.

> But they are (presumed under this model to be) splitting.

Okay, but what's the actual model here? Let's talk about two different versions of many-worlds:

Version 1: Universes splitting

Version 2: No "splitting" per se ever actually occurs, universes are identical up to time t, different thereafter

Is there any difference between 1 and 2 from a physics perspective–any difference in the maths, or in conceivable results of observation or experiment? Or are they just different ways of wording it? A metaphysical/philosophical difference, but not an empirical/mathematical one?

Also, if the theory is symmetric with respect to time, you'd expect merger as well as splitting, since the former is just the time reversal of the latter – isn't QM supposed to have T-symmetry? Does MWI have T-symmetry?