I've been asked this several times by PM, email, here, etc., so here is my answer:
Mathematically, Senator McCain does not have a majority of the delegates. In practice, his "mercurial" disposition and opposition from conservatives may combine to sideline him. A public meltdown is not out of the question.

Half of the states still have to weigh in on the process.
So, yes, a brokered convention is possible--and not just in a Divine intervention, I believe in an all-powerful God sort of way.
What happens then is anyone's guess. Put aside whatever "we" think about what "they" should do and try to think as if you were a Republican Party apologist. It will be very late in the game. They will want to beat Hillary-Obama (or Obama-Hillary, I don't know, whatever). Stop thinking in terms of what's right, the Constitution, the rEVOLution...wait, never stop thinking about those things...what I mean is just for this one mental exercise: "I'm a Republican and I want to win and ..." If the "and +" = nominate an anti-war candidate because the polls show it is the only way to beat the Ds, then we nominate an anti-war candidate (or whatever the polls a half a year away --eons in politics--tell us). This is just one "for example." For Pete's sake people, stop acting as if any of this has to make any sense in terms of rationales--this is politics! If Paul on the ticket = victory, then, well, they aren't as stupid or evil or whatever you want to think. The powers that be want to still be the powers that be.
Does obsessing over any of this now really help?
Please, FOCUS: we have half of the contests now to compete in and, finally, we have professionals running HQ. This is no time for the grassroots to start acting like the weak link.