How big are the Associated Worlds?

As of the time of the Core War, they’re an oblate spheroid about 3,300 light-years core to rim, 4,100 light-years spinward to trailing, and 2,000 light-years (i.e., the thickness of the galactic plane) acme to nadir. This volume contains approximately 100,000,000 stars, with maybe 10,000 systems connected to the stargate plexus. (The gaps will be filled in later on; in the initial expansion, stargate nexuses were concentrated around things that look “interesting”.)

This does not include the Voniensa Republic, which contains roughly 8,000 systems, rather more tightly woven together; while the Worlds touches the whole width of the galactic arm it is in, the Republic only crosses around a third of it.