Game concept
Dominant Family
The game also links it as Dominant Families, Dominant.
From the game's encyclopedia
A Dominant Family is a Powerful Family that has spread their control far and wide. They are considered the most influential House within a Realm.
A member of a Dominant Family is even better at Political Schemes and is even more likely to get what they want when Interacting with other Characters.
A House must control at least 25% of the Realm to become Dominant.
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.
Dominant Family is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Dominant Family is a Powerful Family that has spread their control far and wide." It is part of Noble Family. The game also links it as Dominant Families and Dominant. 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.