Riverboat
They don't all end up at Stanstead, dealt with plenty of these at LHR, which is set up to deal with them just as well.
However Stanstead is 'prefered' because obviously its out of the way. Have an A340 stuck on one of the remote blocks at LHR and its not that remote!
Heathrow Director is right the BAA would prefer to get rid to somewhere else, saves thier runways being closed, but I have seen plenty of captains insist on going to LHR.