IMTU,
Starports "depend" on several factors...
Largely, I refer to economic and strategic issues.
World "Starports"(as opposed to subordinate or space ports) are either Imperial entirely, locally controlled or controlled by an outside vendor.
This view tends to be supported by the text of most GURPS Traveller products that discuss the actual state of starports. Many ports are constructed under a deal cut by a world who has agreed to allow management of the port to go to the vendor who builds or finaces it until repayment os made. If the repayment fails, the MegaCorp gains ownership in many described cases. Most often Hortelez et Cie IIRC.. Ports in key economic, governmental and military(or strategic) positions are wholly Imperial owned in the fluff.
So IMTU, an important port is generally owned by The Imperium unless I the world is both rich, important and the fief of an important noble(IE: Regina). In the case of such ports, they are locally owned and operated or vetted for management contracts by the locals. Lesser ports in key areas are, again, owned and operated(or cotracted out) by The Imperium where other ports are either Corporate owned or locally owned.
Corporate ownership occurs where worlds want a port but do not have the economic pull to do it themselves or get government aid. Also, some ports are owned to control access to a region. For example, IMTU bitter bidding contests are being held between Oberlindes and Tukera in Aramis, Regina, Lanth and Rhylanor Subsectors due to Tukera's attempt to box in and halt Oberlindes' growth. This conflict has spread to both corporate allies of both lines and allied nobility so the blood is being let in certain quarters.
Local ownership is either..
..a port in a system that is rich enough to buy itself out of corporate control
..a port that was profitable but has fallen as the economy moved on and has been abandoned by the corp.
..lesser ports maintained by worlds reaching out beyond their local econmies to try to lure in intersetllar traffic.
Other cases can be made on a world by world basis but the least of the port classes(D and E) are almost always either a local government or on-world corporate facility when they are not just a field near and airport having the cargo storage facilities.
As for "Imperial Turf",
Imperial bases of any kind and Imperial buildings. By and large, the port is where the Imperial Governor for the world lives(in A, B and C ports) and where the Imperial compound is. I treat that as a Consulate property in today's world and, there fore, Imperial turf.
Marc
ps... sorry if one or two items are a bit off as I am typing this from memory. Ex: IIRC, Loel d'Dieu is a world under the thumb of a mega corp and(per GURPS text) fighting to emerge. I did not add that as I am not 100% sure if I am misremembering.