In EU, I believe it went with how each system/sector had its own militarised "police" for local issues. Anything bigger and the various systems were supposed to co-operate and offer up elements of their system forces to combine together under Republic control.
By the time of the Phantom Menace and such, the Republics bureaucracy was just bloated and all the cracks were appearing and systems weren't being as cooperative.
On other funny things: