The universe of the Imperium of the Terran Throne outside the home solar system (of Earth) is largely outside the authority of the regime led by the First Citizen occupying the Terran Throne, though the Imperium of the Terran Throne does control parts of the solar systems of Bernard's Star and Alpha Centauri, which are 6 and 4.3 light years from Earth, respectively. The control of the Imperium outside Earth's solar system is limited to Alpha Centauri and Bernard's Star is both assured and limited to the fact that starships can travel as high as 15 times the speed of light (see technology in ITT universe).
The Imperium of the Terran Throne has an official province (see Government of Imperium of the Terran Throne) in this solar system with three stars (Alpha Centauri A and B and Proxima Centauri), though it's sphere of control is mainly in the Alpha Centaurui Kuiper Belt and Oort Cloud, especially the area near Proxima Centauri. The Alpha Centauri system includes five planets, not including the dwarf planets in the local Kuiper Belt and Oort Cloud. These five worlds are called Centauri I, II, III, IV, & V. Centauri I and II are gas giant planets less than 1 AU (the distance between Earth and it's Sun is 1 AU) and have only a few moons each. The only inhabitants of these moons are A.I. robots and computers, and they are alternately friendly and hostile to the populations of Centauri III and IV and the Imperium of the Terran Throne. Centauri III and IV are 1.2 AU from Alpha Centauri A and B and are both Earth-like double planets that orbit each other. Centauri III has a unified world government elected by all it's inhabitants (humans, chimeras, and A.I. machines). Centauri IV is politically divided into four nations which all have racist governments that discriminate against certain sentients. In one nation, only clones (both humans and chimeras) can vote for the government, leaving natural-born humans and A.I. machines without a voice. In another nation, A.I. for robots and computers is banned. The other two nations of Centauri IV allow only natural-born humans to elect their governments, though they allow cloned humans, chimeras, and A.I. machines to govern themselves as autonomous communities. Centauri V is a planet with two moons, with all three of these worlds composed of rock and ice, though Alpha Centauri V is still six or seven AU from the local Kuiper Belt. The Imperium of the Terran Throne and Centauri III have occasionally fought over control of Centauri V and it's two moons, though the forces of the Terran Throne currently control all three bodies. The capital of the Imperium's Alpha Centauri Province is a Pluto-like dwarf planet slightly larger than Earth called Centauri Prime located in the local Oort Cloud in the vicinity of Proxima Centauri, and both the planet and Proxima Centauri orbit Alpha Centauri A & B with similar speeds and orbits.
This red dwarf star has no planets (except for Ceres- and Pluto-style dwarf planets), but is orbited by a gigantic asteroid belt that begins less than 1 AU from the local star but extends out for over 50 AU and starts out like the asteroid belt between Mars and Jupiter but ends up being an icy Kuiper Belt. The Imperium of the Terran Throne theoreically governs the entire solar system of Bernard's Star as it's Bernard's Star Province, but in practice the Imperium's control is only solid in the local Kuiper Belt and Oort Cloud. The twin capital's of the Bernard's Star Province are the twin dwarf planets Stygia and Spectra, whiuch orbit each other in the local Kuiper Belt. Control of the local solar system is contested by the Free Belt League of Bernard's Star, a democratic republic that is actively anti-Imperium.