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What your maximum hand size is (or whether you even have one) matters only during the cleanup step during the ending phase of your turn.

The effect doesn’t wear off until just before your next untap step (even if an effect will cause that untap step to be skipped). Effectively, that means it removes your maximum hand size just during the turn in which you set it in motion.

If multiple effects modify your hand size, apply them in timestamp order. For example, if you put Null Profusion (an enchantment that says your maximum hand size is two) onto the battlefield and later set this scheme in motion, you’ll have no maximum hand size until your next turn. However, if you set this scheme in motion and then put Null Profusion onto the battlefield that turn, your maximum hand size would be two.