No. The homeworld squares are picked at random around the universe before any planets are spawned. There are some restrictions on location, like an HW can't be placed in an empty space square, or a black hole, etc. Their locations remain fixed throughout the game. When a player joins a game the free HW sector list is scanned and the sector which has the highest avg distance from all other players is selected and assigned to the joining player. Players were irked in beta when they occasionally started right next to somebody, so we tried to space people out more. It is still possible to get a starting position that is terrible. It is also possible to get a starter system that has 5 Terrans, although it is pretty rare.