The norm is to create another bnet account, and start over. People have had some (very minor) success in getting banned accounts removed from their bnet account; however, by and large, Bliz refuses to do this, nowadays.
If you do a forum search, there is plenty of information about the success of getting banned accounts removed.
I've tried to move several banned accounts off a b.net account with no success. Any account in good standing I've been able to move just fine, but any banned account has been a no-go...and I've tried several times.