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So, when a Battle Master is KO'd, does it count as a KO since they are technically not sent to the KO pile? Or is the instance of "KO" simply contingent on reaching your HP total?

It is a KO and they go to the KO Area, before flipping to its Upgrade side.
Source: Wizards of the Coast (2019-04-12)    【Link to Ruling】
Tags: Battle Master, KO