Let's try to explain this:
When Link gets sent back in time, he was able to stop Ganondorf from taking over Hyrule. As such, all the things that happened in the future, as in exploring the Sage Temples, Zora Domain freezing, Volvagia's resurection, etc...none of that happened in the Child Timeline, but it still happened in the Adult Timeline. That is what causes the split.
This does mean that there is no descendant of Link in the AT, but if you read the conversation between the King of Red Lions and Jabun in the Second Quest of WW, which is on the AT, you'd see that WW Link has no relation to OoT Link. There's a new family of heroes in the AT.
This is just the basics. I'm not much of a timeline expert, but this here is all pretty much canon. If you want more detail, try looking through the other timeline threads and whatnot. Beware though, there's a lot more detail to all of this than what I've written here.