Parallel worlds come into existence almost every second of every day. Each decision you make creates a parallel existence, a different dimension where things end up almost the same or...evolve into something completely different. New Earth AU from S3

What if Hatter didn't go through the Looking Glass, but instead sought alternate means of travel? Or, had in land in front of him, whatever.

DW & Syfy's Alice -- No such thing exists, even in Wonderland. But how else do you describe the Doctor?