Establishing Control results in a Conquer if that player has not yet scored this Battlefield this turn. See rule 185. Control for more information on Control. See rule 464.1. for more information on Conquering.
§ 461.5.d Core Rules PDF (officieel)
§ 461 Step 3: The Resolution Step
§ 461.5 1. If no Showdown or Combat is staged at this location, the player with Units remaining here Establishes Control.