Who becomes king or queen in this instance?

For a prime example of this situation have a look at the family tree of George lll (The mad one) his 2 eldest son's became King in turn George lV (The Prince Regent) his only child Princess Charlotte died before him so the crown ped to his next younger brother Prince William Duke of Clarence who became King William lV, he died with no legitimate children. The Crown then would have gone to the next Brother Prince Edward Duke of Kent but he was already dead so the Crown ped to his only Child Victoria.