From the game's encyclopedia
Nomads who want to gain a Title of a higher Tier without Migrating have the alternative of fighting the local inhabitants of an area over a title, as long as they have the right Dominance level.
If there is someone holding the title in question, they will begin a war against that target, to usurp the title from them. If there isn't anyone holding the title in question, they will instead fight every single non-Tributary, non-Ally in the De Jure area of the title.
On a victory, the aggressor will gain the title in question, and all defenders will become their Tributary. On a loss, the aggressor will pay GoldGold to the defender, and lose a significant amount of DreadDread.
If the Decision taker holds the whole De Jure area, they will simply gain the title immediately, as there are no defenders to be fought.
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.
Dominate Title is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "Nomads who want to gain a Title of a higher Tier without Migrating have the alternative of fighting the local inhabitants of an area over a title, as long as they have the right Dominance level." It is part of War. The game also links it as Domination War. Patch 1.20.1.2, from game/common/game_concepts/mpo_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/mpo_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.