Tidus, Yuna's Guardian

To move a counter from one permanent to another, the counter is removed from the first permanent and put on the second. Any abilities that care about a counter being removed from or put onto a permanent will apply.

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.

You don't have to choose every permanent or player that has a counter—only the ones you want to add counters to. Since "any number" includes zero, you don't have to choose any permanents at all, and you don't have to choose any players at all.