If an opponent conquers a battlefield on their turn, then on my turn I charm their unit to my battlefield, and they respond with Ride the Wind to move it back to their original battlefield, do they conquer and score that battlefield again?
Answered under Unleashed Rules FAQ and Clarifications
If your opponent can legally play in response and the opponent's battlefield became Uncontrolled while their unit was on your battlefield, then moving the unit back can cause them to gain Control and thereby Conquer and Score that battlefield on your turn. Whether that actually happens depends on timing — specifically whether the battlefield ever became Uncontrolled while the unit was off it, and whether was playable at that moment.
Yes — provided two conditions are met: (1) the battlefield became Uncontrolled while the opponent's unit was on your battlefield (for example, no other units or combats were present and the game reached an Open State), and (2) the opponent was legally able to play at the time they played it. If those conditions are true, the opponent gaining Control by moving their unit back will cause a Conquer and Score because they have not yet scored that battlefield this turn . If either condition is not met (for example, the battlefield never became Uncontrolled, or could not legally be played in response), then simply moving the unit back will not create a new Conquer/Score.
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