Looking for information regarding police responsibilities towards providing travel home from court for those picked up on a warrant outwith there own local authority area.

There is none, if the person is arrested outside of their county ( or state) and transported back to that jail. There is no libility for them to return them. If they are put in prison, it varies by state, and some locations may have local rules. But if they are released, the door is opened and they walk out, and what happens then is up to them.