My restarts happen even without iTunes running and I don't have an iPhone.
You can see from this thread, that every kind of Mac can get this problem, and there's no solution here either!
http://discussions.info.apple.com/thread.jspa?threadID=2215322&start=0&tstart=0
People seem to try various things, and eventually the problem seems to be solved, and then it starts again. I would argue that this pattern of behaviour is the same whether you try any non-hardware-based fixes or not. In the link above, someone (with an iMac) even had their PSU replaced by Apple and that didn't solve it.
My Mac Pro is due back soon. They thought it might be the PSU or the motherboard that needed replacing. Seems like they were having a best-guess rather than identified the precise cause. In the end, the fact that the fans were also spinning wildly in cunjunction with some of the random restarts, made them think that it was more likely to be a motherboard problem so they have replaced that.
Will keep posting here with updates once I get the Mac back.
Footnote: my Optiarc optical drive also stopped working shortly before it went in for repair. Could that possibly be caused by whatever is causing the restart problem? Also, I'm told the replacement drive Apple sent, arrived faulty. Hence there's a delay while they order another.