If Hitler had been captured by the Allies alive, would he have been executed and when?

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In an alternate history where he gets captured by the Western Allies (maybe after some kind of attempted retreat to the Alps or Norway?), he gets hanged at Nuremberg. If he's alive captured by the Soviets there's a bit more of a question, but I agree with others in the thread: They may not have bothered with the formality of a trial with him.