You can choose any permanent that has a counter, including ones controlled by opponents. You can choose any player who has a counter, including opponents. You can’t choose cards in any zone other than the battlefield, even if they have counters on them.

You don’t have to choose every permanent or player that has a counter—only the ones you want to add counters to. Since “any number” includes zero, you don’t have to choose any permanents at all, and you don’t have to choose any players at all.

If a player or permanent has more than one kind of counter on it, and you choose for it to get additional counters, it must get one of each kind of counter it already has. You can’t have it get just one kind of counter it already has and not the others.

Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it’s too late for anyone to respond.

Some spells and abilities that cause you to proliferate may require targets. If each target chosen is an illegal target as that spell or ability tries to resolve, it won’t resolve. You won’t proliferate.

Atomize : règles, fonctionnement et interactions (MTG)

Atomize 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

Destroy target nonland permanent. Proliferate. (Choose any number of permanents and/or players, then give each another counter of each kind already there.)

How it works : Atomize

Original English text — Wizards of the Coast / Scryfall

#1March 8, 2024· Wizards of the Coast
You can choose any permanent that has a counter, including ones controlled by opponents. You can choose any player who has a counter, including opponents. You can’t choose cards in any zone other than the battlefield, even if they have counters on them.
No other card is named in this ruling.
#2March 8, 2024· Wizards of the Coast
You don’t have to choose every permanent or player that has a counter—only the ones you want to add counters to. Since “any number” includes zero, you don’t have to choose any permanents at all, and you don’t have to choose any players at all.
No other card is named in this ruling.
#3March 8, 2024· Wizards of the Coast
If a player or permanent has more than one kind of counter on it, and you choose for it to get additional counters, it must get one of each kind of counter it already has. You can’t have it get just one kind of counter it already has and not the others.
No other card is named in this ruling.
#4March 8, 2024· Wizards of the Coast
Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it’s too late for anyone to respond.
No other card is named in this ruling.
#5March 8, 2024· Wizards of the Coast
Some spells and abilities that cause you to proliferate may require targets. If each target chosen is an illegal target as that spell or ability tries to resolve, it won’t resolve. You won’t proliferate.
No other card is named in this ruling.