Most likely inspired by Murdoch selling off the lion's share of Fox and just keeping the shitty news company.

I'd guess that Logan is successful in cutting the kids out, sells everything except ATN which he takes personal control of, and it's up in the air whether the kids even get a golden parachute. I'd guess Greg and Tom will have a moral choice over whether or not to take roles at ATN under Logan, it's open to them if they want it.

Logan pretty clearly seems to have ruled out each of the kids for the top job, and like Hyman Roth in Godfather pt2, he's planning as if he's going to live virtually forever. He appears to already be baking a new batch of Roys.