I was dueling in a local tournament and a situation came up. What happens to a monster equiped with snatch steal that is fliped face down with book of moon or tsukuyomi? Does the monster returns to its original owner or does it stay in its current side of the field? Another question is what happens if a player activates lightning vortex and the opponent links enemy controller to take over an opponent's monster, is the opponent's monster destroyed by the effect of lightning vortex?

If “Tsukuyomi” or “Book of Moon” is used on the monster “Snatch Steal” is equipped to, “Snatch Steal” will be destroyed since the effect of “Snatch Steal” only applies to a monster that it is equipped to in Face-up attack position. The monster equipped to “Snatch Steal” would not be destroyed when you have used “Tsukuyomi” or “Book of Moon” on the monster since the monster is switched to Face-down defense position and "Snatch Steal"'s effect don't apply anymore.
Your opponent would gain control over the monster since the monster would no longer be Face-up on your side of the field when "Lightning Vortex" resolves.

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