Which GM, in his current tenure, has signed AND bought out the most players?
Poile?
Great selection, just by statistical likelihood. Poile has been with the team since its inception, 1997. Capfriendly shows they have bought out 9 players in totality (hi Dicky!).
That's probably the highest raw total for any one tenure, but a pretty low rate, considering how many signings he has done (296). Lou Lamoriello comes close during his Devils tenure.
The really fun one is Brad Treliving who has signed 141 contracts and 6 buyouts already. Chris Tanev and Jacob Markstrom might not be far behind if he still has a job.