Game concept
Powerful Family
The game also links it as Powerful Families, Powerful.
From the game's encyclopedia
A Powerful Family represents one of the most influential Houses and Noble Families in a Bureaucratic Realm.
A member of a Powerful Family is better at Political Schemes and is more likely to get what they want when Interacting with other Characters.
There can only be a limited number of Powerful Families at any given time, and it is the top rated Noble Families that are considered powerful based on their Rating. The House of the Top Liege is an exception, which is always considered Powerful.
A Family controlling a significant part of a Realm's land can become a Dominant Family.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Powerful Family is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Powerful Family represents one of the most influential Houses and Noble Families in a Bureaucratic Realm." It is part of Noble Family. It covers Powerful Family Rating. The game also links it as Powerful Families and Powerful. Patch 1.20.1.2, from game/common/game_concepts/07_ep3_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/07_ep3_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.