“Relinquished”’s effect to equip itself with a monster can only be activated during your Main Phase 1 or 2 since it is a Ignition Effect.
A monster equipped to “Relinquished” occupies a Spell & Trap Zone of the controller of “Relinquished”. So if you already have 5 Spell & Trap Cards on the field you cannot activate the effect of “Relinquished”. Any Equip Spell Cards equipped to the selected monster are destroyed. “Relinquished” gains the ATK and DEF of the monster equipped to it, but not the effects of an Effect Monster.
The selected monster is treated as a Monster Card when it is sent to the Graveyard, so the effects of “Sangan” or “Witch of the Black Forest” would activate, but the effect of “Mystic Tomato” would not, since it was not destroyed as a result of battle.
You can not voluntarily destroy a monster equipped to “Relinquished” but you can use “Mystical Space Typhoon” or “Emergency Provisions” to eliminate it.
“Relinquished” will only inflict its effect damage to your opponent if “Relinquished” would be destroyed as a result of battle and the equipped Monster Card is destroyed instead. When this occurs you inflict damage to your opponent equal to the Battle Damage that the controller of “Relinquished” received; this is the ONLY time “Relinquished” will deal effect damage. (If “Relinquished”, equipped with a 1800 ATK monster, attack a 3000 DEF Defense Position monster, “Relinquished’s” controller takes 1200 damage but “Relinquished” does not inflict effect damage to the opponent.)
You can activate “Barrel Behind the Door” against Trigger Effects like “Lava Golem”, “Giant Germ”, “Relinquished” (when it inflicts effect damage, since “Barrel Behind the Door” can be activated during the Damage Step because it is a Counter-Trap Card), “Minar” (when discarded), “Parasite Paracide” (when it inflicts effect damage), “Bowganian”, “Mushroom Man #2”, “Reflect Bounder” (when it is attacked), “Shinato, King of a Higher Plane” (when it attacks and destroys a Defense Position monster and sends it to the Graveyard), “Granadora” (when destroyed and sent to the Graveyard), “Balloon Lizard” (when destroyed), “KA-2 Des Scissors”, “Needle Burrower”, “Atomic Firefly”, “Elephant Statue of Disaster”, and “Ameba”.
Your opponent cannot target your “Blindly Loyal Goblin” with the effect of “Relinquished” or “Thousand-Eyes Restrict”.
While “Gorgon’s Eye” is active, if “Relinquished” equipped with a monster is in Defense Position, the effect of “Relinquished” is negated, it can no longer be equipped with a monster, and the Monster Card equipped to “Relinquished” is destroyed and sent to the Graveyard.
If your opponent takes control of your monster with “Snatch Steal”, etc., and you activate “Relinquished”’s effect on your next turn to equip the monster to “Relinquished”, and your opponent chains “Remove Brainwashing” to “Relinquished”’s effect, control of the monster returns to you before “Relinquished”’s effect resolves and, since you cannot use “Relinquished”’s effect on monsters on your side of the field, “Relinquished”’s effect disappears.
Monsters equipped to “Relinquished” while “Skill Drain” is active are negated and destroyed because “Relinquished” no longer has an effect that allows it to be equipped with a monster, and “Relinquished”’s ATK and DEF are returned to normal.
While the effect of “Timidity” is active, you cannot destroy a face-down Monster Card equipped to “Relinquished”.
“Token Thanksgiving” will destroy a Monster Token equipped to “Relinquished”.
Netrep Rulings:
“Relinquished” may equip itself with one monster at a time per turn.
“Relinquished’s” equipping effect is a targeting effect.
Judge List Rulings:
A face-down card equipped to “Relinquished”/”Thousand-Eyes Restrict” is a legal target for “Nobleman of Extermination.” Curtis Schultz, 03/09/2005
A face-down card equipped to “Relinquished”/”Thousand-Eyes Restrict” will be returned to its owner’s hand by “Byser Shock’s” effect. Curtis Schultz, 03/09/2005
GoatRulings.com Rulings:
Q: If I summon “Relinquished” and use its effect, what happens if my opponent chains a card that would flip-down or remove “Relinquished” from the field?
A: For this example, say you declare the effect of “Relinquished” and your opponent chains “Book of Moon” to the effect. “Relinquished” would be chain link 1 and “Book of Moon” would be chain link 2. In Yu-Gi-Oh! chains always resolve backwards. “Book of Moon” will resolve first, flipping down “Relinquished”. “Relinquished” needs to be face up on the field to attach a monster to itself, so its effect will “fizzle” and the targeted monster will remain on the field. This applies to cards such as (but not limited to) “Book of Moon”, “Ring of Destruction”, and “Compulsory Evacuation Device”.