The Master, Transcendent

Rad counters don't go away as steps, phases, or turns end. They only go away when an effect instructs a player to remove rad counters from themselves.

There is an inherent triggered ability associated with having rad counters. This triggered ability has no source and is controlled by the active player. The full text of this ability is "At the beginning of the precombat main phase of a player with rad counters, that player mills cards equal to the number of rad counters they have. For each nonland card milled this way, that player loses 1 life and removes one rad counter from themselves."

In a game using the shared team turns option, such as an Archenemy or Two-Headed Giant game, the inherent triggered ability associated with rad counters triggers once for each player on the active team that has rad counters. Each instance of that ability is controlled by one of those players.

The Master's last ability will override any characteristic-defining abilities the creature has that set its power and/or toughness. For example, if you put a Robobrain War Mind onto the battlefield with The Master's last ability, its base power and toughness will be 3/3, and the number of cards in your hand won't affect its power at all.

Any effects (such as proliferate) that interact with counters a player gets, has, or loses can interact with rad counters.

Rad counters are a kind of counter that a player may have. They're not associated with any specific permanents.

If a player is instructed to put a card into their graveyard from their library without using the word "mill," (by the effect of Rowan's Grim Search from Wilds of Eldraine®, for example), that card isn't a legal target for The Master's last ability.