Shipbreaker Kraken

Monstrous isn't an ability that a creature has. It's just something true about that creature. If the creature stops being a creature or loses its abilities, it will continue to be monstrous.

If you lose control of Shipbreaker Kraken between when its last ability triggers and when that ability resolves, the target creatures will become tapped. However, they won't be affected by the other effect and will untap as normal during their controllers' untap steps.

An ability that triggers when a creature becomes monstrous won't trigger if that creature isn't on the battlefield when its monstrosity ability resolves.

If another player gains control of Shipbreaker Kraken, the creatures will no longer be affected by the effect preventing them from untapping, even if you later regain control of Shipbreaker Kraken.

If you gain control of a creature that's being prevented from untapping, that creature won't untap during your untap step for as long as you control Shipbreaker Kraken.

The ability can target a tapped creature. If a targeted creature is already tapped when it resolves, that creature just remains tapped and doesn't untap during its controller's untap step.

Once a creature becomes monstrous, it can't become monstrous again. If the creature is already monstrous when the monstrosity ability resolves, nothing happens.