[photon]

Rand created the black tower for all the men who could channel to train them. He appointed Taim to head it and teach the men. The taint is cleansed, so the men aren't getting any more mad.

Then Rand didn't have a lot to do with the black tower other than taking some of the men around with him, but basically left it to itself. There's a lot of innuendo in the previous books that there's something not right going on at the black tower. Lots of hints that Taim isn't behind Rand (Lews Therin basically tries to kill Taim all the time, trying to grasp the power away or before Rand).

Logain was a false dragon who was caught and gentled by the white tower, but then was healed by Nynaeve (so he could channel again). He escaped I think and ended up (with Rand's consent/protection) at the black tower as well as one of the men there.