Parallel universes are just slices of the "real" universe offset in different timelike directions from the slice we experience. I.e, think of time as N dimensional where N > 1, if time were 3 dimensional we could call the timelike dimensions t, t', and t". Our perception is limited to t (plus x, y and z). Moving in the t' or t" axes, we get to parallel worlds (also known as travel "crosstime" in many sci-fi stories). QM effects can propagate crosstime, but we can only observe one slice of that.
There's no actual "split" when a wave collapses, the parallel world(s) was (were) always there, it (they) just hadn't differentiated yet. (There's also no preferred t-like axis -- an observer travelling along t' (with fixed x,y,z) will see a progression of changes just as one at the same (x,y,z) would see travelling along t or t" -- but they'd be different changes.)
Niven had the right idea with his "All the Myriad Ways", the TV series "Sliders" was close too. The idea that there's only one (or at most a handful of) parallel world(s), like ST's mirror universe, is just silly.
And yes, I'm making this shit up (although not entirely). It's part of the background to my paratime stories.