I updated this post to be easier to access, and clarified some of the language.
In the Many Worlds interpretation, the universal quantum state is a giant superposition of all objects in the universe:
There is no ‘wave function’ collapse in this interpretation, so everything remains entangled. How then does this universe ‘split’? The usual story says that a measurement process yields several possibilities, much like the different possible sizes of the triangle below:
And it is these different possible outcomes that define how the universe splits into separate worlds, each corresponding to one of the outcomes:
But the problem is that in order to define a measurement process that yielded the clearly defined triangle outcomes, we assumed that there were distinguishable objects in our universe. Specifically, here’s what we needed in order to get those well-defined outcomes:
(1) a system that can have ‘triangle’ properties
(2) a large number of other, distinguishable systems that can measure those properties
(3) a clearly defined, force-based interaction…
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Transactional Interpretation 
Many Worlds was a first attempt at a model consistent with observation & Bell’s inequality. Fortunately, there are finite, local, & causal multiverse models to solve the problem.
Thanks. Can you clarify how the models you mention solve the problem discussed in the post? I haven’t seen a solution other than simply assuming, as an initial condition on the universe, that the ‘split’ happens in the basis we want it to. For a more technical discussion of the basic logical problem, see https://arxiv.org/abs/1603.04845