Cayth, Famed Mechanist

When you proliferate, you can choose any permanent that has a counter, including ones controlled by opponents. You can choose any player who has a counter, including opponents. You can't choose cards in any zone other than the battlefield, even if they have counters on them.

Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it's too late for anyone to respond.

If you can't put a +1/+1 counter on the creature for any reason as fabricate resolves (for instance, if it's no longer on the battlefield), you just create a Servo token.