I thought for a time that our awareness of other possible situations hinging on our decision is where the universe divides. Like we can pick up on other possibilities, or perceive universes, and merge with them, and the one we most think about or end up doing in the end is where we've crossed the universe into another, where if we'd have pursued another path of existence, we would exist down that path.
Once the thought is conceived, depending on momentum of previous decisions, it will or will not be persued, depending on the sum of all our influences thus far. When we are in indecision, we are splitting the world into two possibilities. From there, chaos occurs based on other people's decisions and so on, allowing for only one resolution, because going either way will be one choice, and going both would be one choice.
Really though, with chaos, everything is just a part of a solution of a huge problem, and there can only be one solution, or one sum of a series of events, but with respective ways to arrive at the solution at any given point in the problem, depending on the depth you've reached. That is, since we make the decisions we do, and we are assumed to have had the same histories in parallel universes, we will make the same decisions, or arrive at them, and so nothing could split our universe. It would have to be self-sustaining, or composed of matter tuned to the same frequencies, or roughly the same.
The only way we could actually split the universe is if we went back into time somehow and disrupted the flow of time and momentum in some way that would later impact our life enough to change our decision. Then, if that disruption didn't lead to the end of time travel, you could travel back into the time you came from having changed the world... though it's hard to say whether it would impact your existence or create another universe. Where would the matter come from? It would only serve as a framework of energy that had changed at one point in its resolving itself, creating a different solution.
Wow... it's a lot of possibilities, but only because it hasn't happened yet. It can only end up in one way.