It is the board's job to appoint the CEO. There are subcommittees formed to do this, which the existing CEO usually stays away from, because in almost all cases

It is the board's job to appoint the CEO. There are subcommittees formed to do this, which the existing CEO usually stays away from, because in almost all cases there is a reason the CEO is stepping away/being made to step away in the first place. Heck even in Steve Jobs' retirement letter (https://www.apple.com/newsroom/2011/08/24Letter-from-Steve-Jobs https://www.apple.com/newsroom/2011/08/24Letter-from-Steve-J...) he didn't appoint Tim Cook CEO but rather "strongly recommended" him to the board.