Does my opponent score a conquer point if I move their unit to a battlefield?

Ruling: Yes, the unit's controller applies contested status when their unit moves to a battlefield, even if an opponent moved that unit there. This means you can give your opponent a point during your turn by moving their unit (such as through charm effects) onto a battlefield.

Sequence:

• A unit moves to or is played to a battlefield
• The unit's controller applies Contested status (if the battlefield is not already contested and they don't already control it)
• The unit's controller gains control of the battlefield after establishing Control

Nuances:

• The player who moved the unit is not necessarily the one who applies Contested status - it's always the unit's controller who applies it