Balthan'gar just seems to be one of the most useless Forsaken, with only Asmodean being worse.

From what I know of AoL Balthamel, he was an anthropologist who liked to study primitive societies, and a womanizer with a gambling problem. He doesn't seem to pay much attention to anything outside his own interests, implied by this passage from WH:



Sounds like Balthamel was an absent-mined academic who liked to get lots and lots of tail on the side. I have no idea if he even had any major personal ambitions since he got killed by a tree about 5 minutes after being introduced to us, and as Aran'gar is too busy following the DO's orders.

Aran'gar does seem to want to bump off the other Forsaken and take over, perhaps after having some fun with Graendal, but has no real plans in place to do so. She just seems to want to take advantage of whatever opportunities shes thinks are presenting themselves. However, she doesn't even seem to follow even her own orders very well, given that Egwene didn't fall very firmly under her control, and then managed to slip out of it. My guess is that Moridin will send her out on some suicide mission if she doesn't actually get executed for her failures; with the end approaching, he seems to be weeding out some of the more incompetant Forsaken and setting up their deaths.