An Imvrassian Hegemony is an autonomous monarchical state within the Empire, usually a former imperial state or a Kingdom and has its own monarch with the title of Sebastokrator.
A Hegemony has full inner workings of government and administrative issues, though united by allegiance to the Crown.
The Sebastokrator has the right to be the head of his own dynasty and to create and give titles to his relatives, to his officials and to his nobles.
The administrative division of the Hegemony follows the local political tradition and furthermore the Sebastokrator is the head of the government of his realm or he can appoint an official with the title of Chartoularios and the title of Count or Protosebastos to run his own government.
The official style of a Sebastokrator/Sebastokrateira is His Royal Highness Sebastokrator/Sebastokrateira (name), Hegemon of (name of the Hegemony). The title of Sebastokrator as a monarch comes immediately after that of a Co-Emperor, but isn't considered superior to the title of Caesar because the latter belongs to the Heir to the Throne.
Also the Heir of the Hegemony has the title of Megas Archon.
One such example of an Imvrassian Hegemony is Urabba Parks.