Individuals do not own planets. If an individual owns more than 50% of the flats then it will be uncontrolled. In the case of a comet, or other body that is one 1 square, whoever owns the city basically has control.
Be aware that whoever controls the system (or if there's no system control, sector) will still have A/E jurisdiction for the comet if it is uncontrolled (I think. Haven't paid as much attention to the new A/E rules).
one last question-can i build on it without permission or do i as i suspect need to apply for permission from the faction who has govenment in the sector???
If there is no slab already on the comet, then you can lay a slab freely. If there is a slab, then you need permission from the person who owns the slab to construct facilities.
There might also be a hidden slab there, if there appears not to be anything on the Galaxy Map.