I conceive the Galactic Republic as having an all-encompassing degree of influence in the most of the Core Worlds by the time Episode I: A True Knight takes place...except for Alderaan. Amongst the Core planets, Alderaan is the last holdout of an earlier age, when each world was governed by its own indigenous rulers. It's like the relationship between France and Monaco, with France being the Galactic Republic and Monaco being the Kingdom of Alderaan.

The Mid Rim also contains many Republic-controlled worlds, though some independent pockets persist. The Outer Rim is more or less beyond the reach of the Republic...except for those rare instances when the Core Worlds are rallied into some sort of concentrated military excursion to the galactic frontier. As a result, all sorts of unsavory elements dominate the Outer Rim, from the Hutt Cartel to the dreaded Clones.