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Omega was trapped in and ruled over a pocket anti-matter universe.
The dimension in which Omega was trapped was located inside a black hole. (TV: The Three Doctors, COMIC: Omega) It was a time trap, meaning no true time passed inside it. In its natural state it appeared as a "crimson bubble of time", (PROSE: K9 and the Time Trap) but Omega could shape this universe as he saw fit through the power of his mind, creating his own paradise in which to dwell.
Over the centuries, however, he grew despondent due to his isolation. The landscape slowly became unstable because of this. Omega planned to escape the anti-matter universe and return to the outside world. However, living inside the universe had a corrosive effect, causing Omega's physical body to wear away. This made it impossible to leave the universe because only his will allowed him to live, and keep it from collapsing. (TV: The Three Doctors, Arc of Infinity)
After the Doctor caused it to collapse in on itself, (TV: The Three Doctors) Omegon learned to create a mobile gateway between his universe and the outside world in the form of a weightless cloud of gas. He filled his world with a depopulated city that acted like a "museum of spacecraft" as he captured starships from across space and time. Now able to control them with his mind from his flagship, he directed the gas cloud to Gallifrey and planned to launch his fleet out of his bubble prison, wiping out the Time Lords in a surprise attack. However, K9 Mark I, come to investigate the disappearance of one of the fleets Omegon had captured, managed to destroy Omegon's flaship, seemingly killing him. He then ferried the stolen ships back to their correct places and times. (PROSE: K9 and the Time Trap)