If Akshan takes a Gear and equips it, and then you move it onto another unit, when Akshan dies does that Gear return to the other player or stay on your other unit but become in their control? How does that work?

When Akshan leaves the board, control of the stolen equipment reverts to your opponent, but the equipment remains attached to your other unit. It does not automatically detach or return to the opponent's unit.

Here is the step-by-step breakdown of how this interaction works:

1. Stealing the Gear: When you play Akshan and trigger his ability, you move an enemy gear to your base and control it until Akshan leaves the board.
2. Moving the Gear: While you control the equipment, you can use an effect (like the Weaponmaster keyword or another ability) to attach it to another unit you control.
3. Akshan Leaves Play: When Akshan leaves the board, his control-change effect ends. Control of the equipment immediately reverts to its original owner (your opponent).
4. The Aftermath: According to RiftJudge FAQ #8714, the equipment does not immediately return to the opponent when Akshan leaves play. Because it is attached to a different unit that is still on the board, it stays attached to that unit.
5. Taking it Back: Now that your opponent controls the equipment again, they can actively move it back to one of their own units by paying its normal equip cost or using their own attach effects. Until they do, it remains on your unit.

(Note: If the equipment had been left attached to Akshan instead of moved to another unit, it would become unequipped and return to the opponent, as noted in RiftJudge FAQ #657. Moving it to another unit is what keeps it attached.)