When can a runner leave the base?

[WestMichiganBlue]

A runner on any base, less than 2 outs, ball hit in the air to the outfield. Runner has tagged and is ready to leave on the catch. But when?

Suppose that hit is sinking line drive, F9 snags the ball and tumbles to the ground and rolls. Does umpire call out as soon as ball is caught - and possibly change it later if fielder does not retain possesion? If Blue waits to make the call, when can the runner legally leave? On the catch? Or on the call?

Situation 2 - ball is bobbled by F9, maybe two or three times before finally securing it. Same questions?

Situation 3 - ball comes out of F9's glove and is caught by F8. Same questions?

WMB