If an account is banned because it's the mocking/spoof type, they get interrogated in order to determine whether or not BOTH accounts should be deleted.
If they're banned because of a straight up AUP violation (usually numerous ones) they've already been warned a number of times and their account is just perished without further warning.
The process is described via the AUP link at the top of every page.
I (or Robert or Phil before me) haven't had to mediate between two members who just couldn't get along. At least not that I can remember off the top of my head. Problem is, in that situation, we'd probably have to ban both if they're both antagonistic. But I'm much more tolerant these days. Years ago, had I the power at the time, there are a few people still lurking around here that I would've nuked. But at this point I'm glad I didn't.