This card can be comboed well with "Tsukuyomi" as it can flip this card face-down every turn, sending whatever monster that is equipped to the graveyard, then you can flip "Relinquished" face-up, allowing you to equip a new monster every turn.
Combining this card with "Ritual Weapon", "The Dark Door" and "Vengeful Bog Spirit" can result in complete domination of the field. For if your enemy's strongest monster were to taken your control, it would gain a additional 1500 ATK, which when combined with "The Dark Door" and "Vengeful Bog Spirit" will give yourself domination in terms of attacking.
Activate "Spirit Barrier" to protect yourself from any battle damage. Combine with "The Dark Door" to ensure that "Relinquished" will not be destroyed after the monster equipped is destroyed.
"Relinquished" creates a strong attack-lock with "Scrubbed Raid". During each Battle Phase (your opponents or your own, after your own attacked), use "Scrubbed Raid" to send the equipped monster to the Graveyard and end the Battle Phase. During your next Main Phase (1 or 2), activate the effect of "Relinquished" to take another monster and equip it. This creates a -1 for your opponent every turn. Even if "Relinquished" is equipped with a weaker or face-down monster, it doesn't matter because "Scrubbed Raid" will prevent all attacks and "Relinquished" will be equipping a new monster next turn anyway. When combined with the effect gained by Tributing "Djinn Releaser of Rituals" (Traditional only), your opponent will be relying on Spell/Trap destruction to break the lock.
"Lava Golem" can be an amusing touch in "Relinquished" Decks, costing your opponent 2 monsters and giving "Relinquished" 3000 ATK.
"Volcanic Queen" can be used as an alternative, as it requires your opponent to have only 1 monster as opposed to 2.
"Grinder Golem" can also be used instead if your opponent doesn't have monster(s), also one of the Tokens can be used for the Ritual Summoning of "Relinquished".
Your "Relinquished" will not be destroyed in battle if it is equipped with an opponent's card. One tactic is to keep a "Relinquished" that is equipped in Attack Position, with "The Dark Door" even when your opponent has a monster with a higher ATK on the field. If your opponent attacks "Relinquished", they takes the same damage from the battle and their stronger card can be adsorbed on your next turn.
Another extension of this tactic is to attack a monster with a higher ATK than your "Relinquished" while it is equipped. The Equip Card will be destroyed, yourself and your opponent both take the battle damage AND their stronger monster can be absorbed during Main Phase 2. This damages your opponent and clears the board of threats.
Though it will prevent the effect of "Relinquished" from damaging your opponent, it is advisable to have "Ritual Cage" on the field when using it. In the event that your opponent is able to destroy the monster equipped to "Relinquished", "Ritual Cage" will prevent yourself from effectively taking a direct attack. "Ritual Cage" will also stop monster effects from targeting/destroying "Relinquished", so that's another plus.
The effect of "Relinquished" is great to clear "Toolbox" monsters off of your opponent's side of the field. Cards such as "Giant Rat" and "Mystic Tomato" will not have their effects activated if destroyed while equipped to "Relinquished" because they were destroyed by the effect of "Relinquished", not by battle. Cards such as "Sangan", however, will still have their effects because they were still sent from the field to the Graveyard.
This card can be brought back from the Graveyard by "Limit Reverse" as long as it was properly Summoned.
Using "Emergency Provisions" with "Relinquished" (especially with a Chain to go with it) will give yourself LP and allow yourself to steal another one of your opponent's monsters (assuming at least a turn has passed since your last steal).
This card works well with "Opti-Camouflage Armor", using your opponent's strongest monster's strength for a direct attack. The aforementioned "Lava Golem" is a great way to capitalize on this.
Alternatively, you can use "Shadow Delver" to allow this card to attack directly.
This combo can be furthered with "Double Attack", allowing it to attack directly twice, and since "Relinquished" is level 1, anything can practically be discarded for the cost.
Revival cards like "Monster Reborn" and "Limit Reverse" can be used to revive "Relinquished" as long as it was properly Summoned onto the field prior to being sent to the Graveyard. As "Relinquished" is a Spellcaster-Type monster, "Magical Exemplar" can be a very efficient way to Summon it from the Graveyard.
If a Ritual Spell that can be used to Ritual Summon "Relinquished" is in your Graveyard, "Preparation of Rites" can be used to retrieve that Ritual Spell and search this card from your Deck to allow for a quick 2nd "Relinquished".
Protect this card from high-Level monsters with "Level Limit - Area B" or "Gravity Bind". Because "Relinquished" is a Level 1 monster, it will still be able to attack your opponent while "Gravity Bind" or "Level Limit - Area B" is on the field, which can damage your opponent if "Relinquished" is equipped with a monster that would not normally be able to attack under these conditions.
The equipped card can be used as a cost for "Release Restraint Wave" to give "Relinquished" a chance to absorb something stronger while also getting rid of any Traps that could be harmful to "Relinquished".
Use "Relinquished" with "Light of Intervention" to always get a boost from whatever monster that was absorbed.
It is possible to attack directly with "Relinquished" each turn by using "Kinka-byo" and "Infected Mail" or just equip it with "Opti-Camouflage Armor".
A fun if strange card that can be used with "Relinquished" is "Unstable Evolution". While your Life Points are lower, "Relinquished" will have its original ATK change to 2400, and if the Life Points should ever get higher then it will still be on 1000 ATK, compared to the normal 0 ATK.
This card can be combined with "Baby Tiragon", so it can do a direct attack.
"Relinquished" Decks lost a lot of power when "Thousand-Eyes Restrict" was banned in the September 2006 List. But it still retains the basic field control aspect.
When a small monster (or a face-down monster, or no monster at all) is equipped, this card can be used with "Crush Card Virus".
"Djinn Releaser of Rituals" works well with this card. By preventing your opponent from Special Summoning monsters, they will be limited to their 1 Normal Summon per turn, which, combined with the ability of "Relinquished" to take their monsters, will often leave them wide open to direct attacks.