I think that the Ardishappur family has nominal governance of all Ammatar lands, with the natives of that area operating semi-autonomously. So on paper they're not Ardishappurian, but in practice, they do defer to the man himself.
No so sure about other regions - remember that the Empire is a very deep Feudal system at heart, so there could be a lot of vassal holders operating under potentially shifting allegiances in regions considered not worth centralised leadership. Low sec and non-hostile border territories especially.
It would be nice to see exactly what the smallest collection of worlds is, that can be considered a fairly stable Royal Holding, as I don't think all regions would have one sole overlord.