Mishra's Research Desk — ruling 1

You must pay all costs and follow all normal timing rules for spells cast using the first ability of Mishra's Research Desk.

Mishra's Research Desk — ruling 2

If you activate a card's unearth ability but that card is removed from your graveyard before the ability resolves, that unearth ability will do nothing as it resolves.

Mishra's Research Desk — ruling 3

Activating a card's unearth ability isn't the same as casting that card. The unearth ability is put on the stack, but the card is not. Spells and abilities that interact with activated abilities (such as Defabricate's second mode) will interact with unearth, but spells and abilities that interact with spells (such as Scatter Ray) will not.

Mishra's Research Desk — ruling 4

At the beginning of the next end step, a permanent returned to the battlefield with unearth is exiled. This is a delayed triggered ability, and it can be countered by effects such as Defabricate that counter triggered abilities. If the ability is countered, the permanent will stay on the battlefield and the delayed triggered ability won't trigger again. However, the replacement effect will still exile the permanent if it eventually leaves the battlefield.

Mishra's Research Desk — ruling 5

Unearth grants haste to the permanent that's returned to the battlefield (even if it's not a creature card). However, neither of the "exile" abilities is granted to that permanent. If that permanent loses all its abilities, it will still be exiled at the beginning of the next end step, and if it would leave the battlefield, it is still exiled instead.

Mishra's Research Desk — ruling 6

If a permanent returned to the battlefield with unearth would leave the battlefield for any reason, it's exiled instead—unless the spell or ability that's causing the permanent to leave the battlefield is actually trying to exile it! In that case, it succeeds at exiling it. If that spell or ability later returns the card to the battlefield (as Static Net might, for example), the permanent card will return to the battlefield as a new object with no relation to its previous existence. The unearth effects will no longer apply to it.

Mishra's Research Desk : règles, fonctionnement et interactions (MTG)

Mishra's Research Desk is one of those cards players keep asking about. Here is, in plain words, what its official text says, the rulings published by Wizards of the Coast, and the combos players actually run.

Official card text

, , Sacrifice this artifact: Exile the top two cards of your library. Choose one of them. Until the end of your next turn, you may play that card. Unearth (: Return this card from your graveyard to the battlefield. Exile it at the beginning of the next end step or if it would leave the battlefield. Unearth only as a sorcery.)

How it works : Mishra's Research Desk

Original English text — Wizards of the Coast / Scryfall

#1October 14, 2022· Wizards of the Coast
You must pay all costs and follow all normal timing rules for spells cast using the first ability of Mishra's Research Desk.
No other card is named in this ruling.
#2October 14, 2022· Wizards of the Coast
If you activate a card's unearth ability but that card is removed from your graveyard before the ability resolves, that unearth ability will do nothing as it resolves.
No other card is named in this ruling.
#3October 14, 2022· Wizards of the Coast
Activating a card's unearth ability isn't the same as casting that card. The unearth ability is put on the stack, but the card is not. Spells and abilities that interact with activated abilities (such as Defabricate's second mode) will interact with unearth, but spells and abilities that interact with spells (such as Scatter Ray) will not.
No other card is named in this ruling.
#4October 14, 2022· Wizards of the Coast
At the beginning of the next end step, a permanent returned to the battlefield with unearth is exiled. This is a delayed triggered ability, and it can be countered by effects such as Defabricate that counter triggered abilities. If the ability is countered, the permanent will stay on the battlefield and the delayed triggered ability won't trigger again. However, the replacement effect will still exile the permanent if it eventually leaves the battlefield.
No other card is named in this ruling.
#5October 14, 2022· Wizards of the Coast
Unearth grants haste to the permanent that's returned to the battlefield (even if it's not a creature card). However, neither of the "exile" abilities is granted to that permanent. If that permanent loses all its abilities, it will still be exiled at the beginning of the next end step, and if it would leave the battlefield, it is still exiled instead.
No other card is named in this ruling.
#6October 14, 2022· Wizards of the Coast
If a permanent returned to the battlefield with unearth would leave the battlefield for any reason, it's exiled instead—unless the spell or ability that's causing the permanent to leave the battlefield is actually trying to exile it! In that case, it succeeds at exiling it. If that spell or ability later returns the card to the battlefield (as Static Net might, for example), the permanent card will return to the battlefield as a new object with no relation to its previous existence. The unearth effects will no longer apply to it.
No other card is named in this ruling.