Game concept
Nominal Duumvirate
The game also links it as Nominal Duumvirates, Nominal Co-Emperor, Nominal Co-Emperors.
From the game's encyclopedia
A Duumvirate is the rule of one Empire by two Characters. A senior emperor (the Liege), and a junior emperor (the Nominal Co-Emperor).
They are considered to be Nominal Duumvirates when the junior emperor is a Child who cannot effectively rule, but will transition into being full Duumvirates when they reach adulthood.
Nominal Co-Emperors generate passive Influence for both themselves and their senior emperor. How much exactly scales up every 5 years in the job, carrying over when they become a full Co-Emperor.
Appointing a Child Nominal Co-Emperor marks them as being trained to one day likely be the senior emperor. The more practice they get, the more training they receive.
This is represented as additional Skill distributed to them when they become an Adult, depending on their Scales of Power swing.
Children do not receive Mandate events.
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.
Nominal Duumvirate is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "A Duumvirate is the rule of one Empire by two Characters." It is part of Co-Rulership. The game also links it as Nominal Duumvirates, Nominal Co-Emperor and Nominal Co-Emperors. 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.