The few centralised functions is on Pell Station. Formed by free merchants with no affection to old Earth and no love for the genetic engineering so common in the Union. A kind of technocracy where the captains of the big merchant ships are the rulers.
The free Merchants already had a problem with the oppression from Earth and also started to oppose Earth. When war broke out between Union and Earth the merchants found themselves on both sides. Some took sides, but most did not want that.
So when the Union was victorius and their centalized rule scared the free merchants even more than the distant Earth, the Merchants decided to rebel against both the Union and the Earth Defence Fleet. That fleet in reality was a fourth power, not really controlled by Earth. One of the captain's in the fleet joined the Merchants and the rebellion became successful.
The Merchanter's Alliance was born and a truce between the Alliance, the Union and Earth was negotiated. The remains of the Fleet vanished and ar belived to act as pirates in some parts of space.