The Milky Way

The TSN has mapped out these rough boundary lines of territory for each race.

Note that the Sagittarius Arm is where the TSN space fortresses are set up.  Due to the aggressive nature of the conflict thus far, very few planets have been colonized directly in this arm.  Most of Earth's initial colonies are still in the Orion Spur.

The Hegemony resides mainly in the Centaurus Arm of the galaxy.  Despite the Hegemony working together, they do have distinct claimed areas of spaces that they primarily defend.  The Torgoth are the gatekeepers between the Centaurus Arm and the Norma Arm where it is speculated that the Skaraan came from.