If only one player’s Units remain at the Battlefield, and if that player does not already Control the Battlefield, that player establishes Control over the Battlefield. See rule 188. Control for more information on Control. See rule 469.1. for more information on Conquering. 1. This results in a Conquer if that player has not yet scored that Battlefield this turn.
§ 348.2.a Core Rules PDF (officieel)
§ 348 If all players pass Focus without playing a spell or activating an ability, then the Showdown Closes.
§ 348.2 If it is a Non-Combat Showdown, do the following: