If you limit it to births to date, it's going to be mostly Africa again, for a different reason. If you were to stick to a few millenniums back it could be interesting, I guess, because agricultural regions will dominate. I would suspect data for the late Paleolithic isn't known with any certainty.
Past a century into the future, it becomes basically all assumptions. Humans are a very prosperous species and it seems likely we'll have descendants on Earth for hundreds of millions of years. Even if we manage to destroy civilisation, any group of survivors could be back up and building cities in a geological instant.
If things stay progressive and prosperous, the natural birth rates are going to collapse because people just don't bother to reproduce. Are we going to do Brave New World baby factories? If we do, population becomes a matter of policy. Unless people migrate far more than today, which doesn't seem impossible, in which case you have to make assumptions about where they'll want to go.