Following the increasing bureaucratization of Thyllanorian government under Malveus II Karthmere throughout his reign, beginning with the Loyalty Edict in the 240s and concluding with the founding of the four primary branches of sub-paramount government upon his death in 272 AC, the notion of the Lord Paramount directly controlling his own duchy became undesired by the lords sworn to him; namely, the ones who were most involved in the movement towards further autonomy and centralization. To this end, Malveus's son, Vicede II Karthmere, officially destroyed the title of the Duchy of Faercrest on May 19th, 287 AC, and in its place established a simple work-around; the land that once composed the duchy would now simply be referred to as the Royal Demesne, as recognition of Thyllanor's increasing invested power within the individuality of its dukes and the feudal oath they swear to the Lord Paramount, who in turn only had to answer to the King of Andoras himself.
The Royal Demesne, in short, is the land that the Lord Paramount controls directly. It is different from its former ducal state in that if the Karthmeres were somehow disgraced or fell from power, they would not retain the seat of the Duchy of Faercrest as their ancestral de jure holdings; it would then go to the next Lord Paramount or King of Thyllanor, who would rule from the Royal Demesne regardless of their former standing or holdings. It is albeit a mostly ceremonial name in the 4th century AC, as Lords Paramount such as Dalan I Karthmere and Dalan II Karthmere have taken an inclined stance on the reformation of pre-Dragomyr invasion Thyllanorian tradition, such as the restoration of the land's former title as the Duchy of Faercrest. Semantically, it means little to the Karthmeres, as they do not seem to be in danger of losing their hold on Thyllanor any time soon; however, some of the more liberally-minded lords and members of government in Thyllanor favor the state of the title -- particularly the principalities, who view it as the first step into establishing an elective majority in Thyllanor's government, and eventually full democracy.
For representative purposes, the land is still referred to as the Duchy of Faercrest. Outside of Thyllanor, the Royal Demesne has little meaning except in Doras Edrossi, where it is recognized in the same way as a city-state's central holding might be.