//The Queen should abdicate and hand over to William.//
1. I would be surprised to see her abdicate though I haven't really thought it through.
2. If she did it would be in favour of Charles. This not being a banana republic, she does not get to choose her successor. The succession is governed by Common Law, with a bit of constraint provided by the Bill of Rights and the Act of Settlement. Charles is the legitimate heir to the throne and he would have to abdicate in favour of his son before he could take over. I think there is very little chance of that.