Game concept
Cadet Branching
The game also links it as Cadet Branch, Cadet Branches.
From the game's encyclopedia
Dynasties always have a founding House, but in order to become House Heads themselves, House members can choose to create their own new House — a Cadet Branch.
Members of such offshoot Houses are free to do the same, eventually leading to a tree of Houses within the larger Dynasty.
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.
Cadet Branching is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "Dynasties always have a founding House, but in order to become House Heads themselves, House members can choose to create their own new House — a Cadet Branch." The game also links it as Cadet Branch and Cadet Branches. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.