All of the access points broadcast a certain SSID. When a client tries to connect, they coordinate with each other to choose which one will reply to that particular client. That is, the client things it is connected to one AP and doesn't know anything special is happening.
If the system wants to move your client to another AP it just disconnects you from the first AP and when you try to reconnect the second AP will reply to you.
In a case like that, assignment is driven as much as "having a clear channel" as "having a better connection on the channel". If you had a choice between two channels, once of which was shared and slightly "better" and another you can have to yourself, you are better off having one to yourself. (That way you aren't having to wait for other clients to stop sending or receiving, dealing with interference, etc.)
A corollary to that is that if you have both 5GHz and 2.4GHz support on an access point you do best distributing clients between both sides, even if people think 5GHz is better or that 2.4GHz performs better in real life.
I am amazed that instead of all the silly gimmicks that APs have been marketed with, nobody has come out with one that has a lot of radios working on different channels and just behaves like a large number of APs. Practically I think this would work way better than channel aggregation.
