Last time I wrote about Taim, now I'd like to write about Logain. Min has this viewing of Logain obtaining Glory, and Egwene has a dream about our good friend Logain Ablar. The first is of Logain, laughing, while stepping over Rands corpse onto a large, black, block, except when he mounts the block Rands corpse collapses. So in my humble interpretation of events Logain takes over the Asha'man (he apparently is stepping onto the the speaking platform at the Black Tower) after Rands apparent death. Now what becomes of Taim I don't know but he has to be out of the way, in order for Logain to take over. Now since I believe Taim is Demandread I can assume he is dead.