Lately, I have seen and heard some issues about where or who's side does an equipped monster or spell goes to. The way I am starting this seems confusing but it'll be easier when I explain it.
Equip Cards always stay on the side of the player who activated it. When the monster's control changes between player, the equip stays in the position of the player who activated it.
A monster MUST remain face-up to wield an Equip Card unless other wise told
A monster equipped with an equip card that is destroyed by battle or effect are NEVER destroyed at the same time unless the effect destroys all cards on the field are destroyed.
When a monster equipped with a Equip SPELL Card (because there are Equip Trap Cards as well), is either removed from the field or flipped facedown, the Equip Spell Card is destoyed. Neither situations count as "an Equip Card destroyed while equipped to a Monster".
Equip Spell Card who's effects depends on the status of the player depends on the player who first activated it, unless its otherwise stated. PM me cards you are uncertain about.
Text: While your Life Points are lower than your opponent's, the original ATK of the equipped monster is doubled. While your Life Points are higher, the original ATK of the equipped monster is halved.
If I activate Megamorph while my LP is lower than my opponent's LP and equip it to Shooting Quasar Dragon, Shooting Star Dragon would have 8000 ATK points.
United We Stand
Text: The equipped monster gains 800 ATK and DEF for each face-up monster you control.
If I have a field with 5 monsters and I activate and equip my opponent's monster with United We Stand, while my opponent has only 1 monster, the equipped monster would get a 4000 ATK boost.
Monsters that Equip themselves.
You have heard of monsters such as Blast Sphere and Mind Jacker, but some people don't understand which side the monsters go to. The controller of the monster always has possession of the monster equipping itself to another monster. If the controller does not have space in his/her Spell/Trap Zone , the monster effect will activate but will stay in the monster zone and be destroyed by battle.
Text: When your opponent's monster attacks this card in face-down Defense Position, the attacking monster is equipped with this card (damage calculation is canceled). Treat this card as an Equip Spell Card. During each of your opponent's Standby Phases, increase your Life Points by half of the ATK of the monster equipped with this card.
When Kiseiti is attack facedown, it will automatically equip itself to the opponent's monster. Kiseiti will rest in the Spell/Trap Zone of its controller, not the controller of the monster it's equipping to.
There also monsters who take monsters on the field and equip themselves with monsters on the field or graveyard. If that happens the monster targeted by the effect will rest in the Spell/Trap Zone of the controller of the monster who is equipping itself. This sounds confusing, but it'll be explained as I go. These monsters are like Relinquished and the Allure Queens.
Text: Select 1 monster on your opponent's side of the field and equip it to this card (this effect can only be used once per turn and you can only equip 1 monster at a time to this card). The ATK and DEF of this card become the same amounts as the monster equipped to this card. If this card is destroyed as a result of battle, the equipped monster is destroyed instead, and any battle damage you received from the battle is also inflicted to your opponent's Life Points.
If Relinquished targets a monster on my opponent's field, that monster will go to my Spell/Trap Zone. Relinquished cannot use his effect if all my Spell/Trap Zones are occupied. If the monster was face-down that Relinquished targeted, the monster will remain face-down in my Spell/Trap Zone and Relinquished's attack and defense will be [0/0]
Text: A monster destroyed by this card as a result of battle becomes an Equip Card at the end of the Battle Phase that increases the ATK of this card by 200 points.
If I control Sword Hunter and it destroys my opponent's monster by battle, I can use Sword Hunter's effect and the monster will rest on my Spell/Trap Zone. If my Spell/Trap Zone is completely occupied, then I cannot use Sword Hunter's effect.
Type: Trap (Normal)
Text: Select 1 face-up monster on the field. Equip this monster with all face-up Equip Cards on the field. If the target of the Equip Card is not correct, destroy the Equip Card.
Equip Cards do not move from their current location by this effect. They'll equip to the new monster from where they are.
Monsters that automatically equip themselves to a monster or are forcibly equipped to a monster are destroyed if they are moved by this card effect because they do not have a specific target they can equip to.
If Union monsters are moved to one monster on the field, the player controlling the targeted monster can choose which Union monster they want to equipped to their monster and destroy the others.
If I missed anything or if you have any questions or concerns, please reply to this topic.