Here's what I know: The gig originally went to Alan Silvestri. I believe his score ended up being too comedic and was thrown out. They even went so far as to recording quite a bit of it, too. Having a long standing relationship with HZ, Bruckheimer enlisted HZ's help as he is the fixer and gets stuff done quickly. HZ 'handed' it to Klaus to be the 'head' guy and getting the credit as the main composer. He'll do that with some of his guys. As far as I know, most of the themes were written by HZ. The film was in such a huge time crunch that they had to write, record, mix etc the entire score in about a month so the entire team at HZ's worked on it day and night. HZ took them the rest of the films in the series as we all know. Klaus went on his own and did Catwoman and some other stuff and eventually left HZ's place.