From TF2 Wiki
If you kill (or assist in killing) a particular player four times without being killed by them in turn, you will receive a Domination, accompanied by a distinct sound cue and a message on the recent kills section of the HUD. In this case, an icon will appear over your head visible only to that player, indicating you to be their Nemesis. If a player you are dominating kills you, they gain a Revenge kill, and you lose your domination and status as their nemesis.
Dominations in one life are counted in your all-time stats. When dominating players, a medal symbol will appear next to your name on the scoreboard along with a number indicating how many opposing players you are currently dominating. Dominations are carried over map stages, but not over team or map changes.
Dominating someone may sometimes produce a domination response, which may be specific to the class you have just dominated. Dominating several people in one round will result in increasingly enthusiastic responses from your character.
Team swapping will cause all dominations for and against you to be lost.
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