There is one general reaction while looking at either Card's text. The first thing everyone notices is not an amazing effect, or wonderful mechanics abuse. It's their HUMONGOUS length. Seriously, they are so long that their font is almost elligible Q_Q
These walls of text also lead to our first ruling on Relinquished:
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.
Notice anything missing? Yes, something is actually missing from Relinquished's text. Notably, it's lacking the clause about only being able to be Ritual Summoned with the Ritual Spell Card "Black Illusion Ritual". Surprisingly, this isn't a typo either, as its Japanese text also lacks this clause. This doesn't mean that you can Normal Summon, Set, or Special Summon Relinquished in any way you want to. It is still a Ritual Monster, so it follows all of their restrictions.
Let's look at its first effect now:
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).
This effect is an Ignition Effect that targets 1 monster on the opponent's side of the Field. It is also the main source of the barrage of individual Card rulings under Relinquished, which devoted to explain how such a weird mechanic worked. It's no wonder to have unique and often contradicting Cards in a game whose second expansion already contained a Card that defied all standards.
Equipping a monster is not as problematic as the amount of rulings make it seem. For starters, you take control of the targeted monster, so it takes up one of your S/T Zones. If the monster is face-up, it is treated as an Equip Spell Card named as the equipped monster, so you can send an equipped "Cyber Dragon" to the Graveyard along with other Machine-type monsters in order to Special Summon Chimeratech Fotress Dragon. However, you cannot send an equipped Machine-type monster, as it no longer has a type while equipped. Only their name is kept. If the equipped monster has an effect that activates when it leaves the Field, it will activate if it leaves the Field as a Spell Card, such as Sangan or Fortune Lady Light.
If Relinquished has its effects negated, it is no longer able to stay equipped with a monster, so the equipped monster is destroyed by Game Mechanics. Also, if Relinquished activates its effect to equip a monster, and Relinquished is flipped face-down or Removed from the Field in a chain, the targetted monster is sent to the Graveyard, as it an equip to Relinquished, so Relinquished nets you advantage even if it's no longer there. Another side note that most people are already aware of is that you cannot simply "dispose" of an equipped monster for no reason just to equip a new one. This used to be a common question ages ago, and I guess it still haunts me every now and then Q_Q
Now, let's look at its second effect:
The ATK and DEF of this card become the same amounts as the monster equipped to this card.
This is a Continuous Effect. Relinquished here reffers to the printed ATK/DEF values of the monster, as none of the monster's effects are applied while equipped. One is often used to consider this the Original ATK of the monster, but for example, Gladiator Beast Laquari modifies its Original ATK. While equipped with Laquari, Relinquished's ATK will always be 1800 and not 2100, since we ignore Laquari's effect. A face-down monster provides 0 ATK and DEF. A Trap Monster provides the ATK/DEF that its text lists. Note that this is Relinquished's effect, and not one of the Equip Spell Card it created, so even if Imperial Order is active, Relinquished will keep its ATK/DEF bonus.This also implies that when Relinquished's effects are negated, its ATK/DEF drops to zero (and loses the Equip Card, as mentioned above). Probably one of the weirdest interactions will be Relinquished vs. Shrink, which results in Shrink having its ATK set to zero until the End Phase. This happens because Relinquished doesn't modify its Original ATK by this effect,and it also tries to force a current ATK value rather than gaining it. Don't worry if you didn't get the last part. Shrink is quite a rollercoaster of rulings. A really boring and malfunctioning rollercoaster >_>
Let's move into Relinquished's last, and most bizarre effect:
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.
Right off the bat, we'll have a hard time figuring what type of effect this is. For starters, these are actually two separate effects, even though they are listed in one sentence, and they are not dependant of each other. The first effect is Continuous, as all substitution effects. The second effect is a Trigger Effect that activates at the "After Damage Calculation" Sub-Step. The first one is somewhat obvious, so let's move into the second one. The most important aspect about this effect is that it does NOT inflict Battle Damage as it suggests. It actually inflicts Effect Damage, so Cards like Prime Material Dragon would prevent it. It is also relevant that if you take enough Battle Damage to lose the Duel, the Duel ends immediatly and Relinquished does not activate this effect, so Relinquished does not produce ties. Like we mentioned at the beginning of this paragraph, the effects are not dependant, so if you take Battle Damage, but Relinquished isn't destroyed in battle, it will still inflict damage to the opponent.
Thousand-Eyes Restrict isn't too different from Relinquished. It loses the damaging effect, but it keeps all the other ones, and gains an additional effect:
As long as this card remains face-up on the field, other monsters cannot change their battle positions or attack.
This is a very simple Continuous Effect. I will say this now and probably repeat it a million times, but effects like this, in general, do NOT prevent position changes from Card effects. They only prevent manual changes. And probably the only other relevant ruling is that if there are two copies of Thousand-Eyes Restrict, no monster can attack or change its battle position. This may seem obvious, but it used to happen a lot back in the day. Oh, the memories...
I guess wraps it up for today. Long article for long texts. Stay tuned for more nostalgia. If you have any questions, feel free to drop me an e-mail at ness00[at]gmail[dot]com.