Are Everettian branchings global or local? Everett's theory of quantum mechanics is about the wavefunction of the whole universe holistically. If a branching occurs very far away at the Andromeda galaxy, do I also branch? Are branchings global or local? If the branching occurs outside the cosmological horizon, do I branch?
 A: in MWI interpretation, "branching", in the sense that systems will spread across many eigenstates over time, always happens locally. MWI helps understand the EPR experiments precisely because it is strictly a local phenomena; separate observers that measure parts of an entangled system will "branch" locally exactly like the distant component did not exist at all. 
Only when both observers join and mutually interact to exchange observation results, their branches will couple selectively to each other in order to preserve globally conserved quantities (like angular momentum)
A: In the many worlds interpretation (MWI) interpretation of quantum mechanics there is just one single wave function for the entire universe.  So there really does not exist the concept of "branching". You can read about it here.
What "branching" really means is that different portions of the wavefunction decohere so that there is no possible communication between the different decoherent portions of the wavefunction.
For example when an electron diffracts and is "detected" in one particular fringe of the diffraction pattern in "our" universe what really happens is that the electron interacts with a large number atoms in the detector and this causes that part (or our branch) of the wave function to decohere relative to all the other portions where the same electron was detected in a different fringe. So, in that sense it is kind of like a branching since our portion of the wavefunction cannot interact with all the other portions which are decoherent.
But there is only one wavefunction for the entire universe so if the universe extends beyond our horizon all of that is also included in the wavefunction of the universe.
A: One thing is for sure. The branchings can't possibly be microlocal. The example of the fractional quantum Hall effect (FQHE) makes this clear. In FQHE, a Landau level band is partially filled with band electrons and they end up in a highly entangled state approximated by something like the Laughlin wavefunction ansatz. The entanglement for this state can be over macroscopic distances of the order of the mean distance between anyonic excitations. If the sample is pure enough, the entanglement can be over the sample size, but typically, there will be "defects" and the defects are none other than the anyonic excitations. If a superposition of an anyon-antianyon pair and no pair is set up, the resulting branching can't possibly be more local than the distance between the anyon and antianyon.
A: Some MWI proponents have tried to get away with an interpretation with no splittings at all, but then, all you are left with is an unstructured Hilbert space which is nothing more than some complex vector space with a norm. Splittings are necessary for MWI to work. This is best done in the Schrodinger picture. How do you define splittings in the Heisenberg picture without secretly smuggling in the Schrodinger picture? It will be an utter mess. Splittings have to respect the quasilocal structure. What other criteria can we have for splittings anyway? Overall, splittings can only make sense locally. Globally, it is always an entangled mess.
