The asteroid itself is roughly the size of the Islands of Great Britain and has several cities all over the asteroid with tunnels extending underground connecting them all. The Mole Men have the ability to survive in a vacumn due to their vacuous nature.
The Asteroid was attacked and most of its cities were destroyed by the Money Spiders in the Battle of Rock, a sub-battle of the Galactic Credit Crunch. Surviving Mole Men fled to Earth, including Mini-Mole and DJ Thursbinator. After the war, the League helped to rebuild the cities on the Asteroid and repopulate it with Mole Men, however, the refugees who had fled to Earth never returned. This created a divide in the species that never healed.