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Splinter Twin grants an activated ability to the enchanted creature. That creature's controller (who is not necessarily the Aura's controller) can activate it. The creature's controller is the player who gets the token.
The token will not be kicked, even if the creature it's copying was.
If the enchanted creature is copying something else when the ability resolves (for example, if it's a Renegade Doppelganger), then the token enters as a copy of whatever the enchanted creature is copying, plus it has haste.
If the token isn't exiled when the delayed triggered ability resolves (due to Stifle, perhaps), it remains on the battlefield indefinitely. It continues to have haste.
If the enchanted creature has in its mana cost (such as Protean Hydra), X is considered to be zero.
The token is exiled at the beginning of the next end step regardless of who controls it at that time, or whether Splinter Twin or the enchanted creature is still on the battlefield at that time.
If the enchanted creature is a token, the new token copies the characteristics of the original token as stated by the effect that put it onto the battlefield, plus it has haste.
Any "enters" abilities of the enchanted creature will trigger when the token is put onto the battlefield. Any "as [this creature] enters" or "[this creature] enters with" abilities of the enchanted creature will also work.
If you activate the ability and the enchanted creature leaves the battlefield before the ability resolves, you still get a token. The enchanted creature's last existence on the battlefield is checked to see what it was (specifically, if it was itself or if it was copying something else).
If the ability is activated during a turn's end step, the token will be exiled at the beginning of the following turn's end step.
The token that's put onto the battlefield copies exactly what's printed on the enchanted creature (unless that creature is copying something else or it's a token; see below), plus it has haste. It doesn't copy whether the enchanted creature is tapped or untapped, whether it has any counters on it or Auras attached to it, or whether it's been affected by any noncopy effects that changed its power, toughness, types, color, or so on. In particular, it doesn't copy the ability granted to the enchanted creature by Splinter Twin.
If the enchanted creature is legendary, you will have to put either the original creature or the token into the graveyard as a state-based action.
