Prisoner transport out here is handled exclusively by the Sheriff’s department. So are warrants too - what with sheriff sales and the tax collection auctions also going through them.
We do have a Constable though. Really nice guy, without much to do. He works all of the election depots. With volunteers, but not as many as you’d think.
In my case as an example, I lived in an unincorporated community of some 40,000 residents. We contracted our law enforcement to the constable's office instead of the county sheriff.