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You can only assign as many hits as a ship can take (so a dark raider with no shields can take 1 hit). This is useful when you have for example one heavily shielded ship but with low firepower, which can take a lot of beating before it gets destroyed, preserving the rest of your fleet.
Thanks for the answer, Andrei!
So, if one ship ends up getting destroyed, but not all hits have been assigned yet, does the attacker then simply get to assign all remaining hits as normal?