I'm wondering when toll roads meet free interstates or other major highways, who is responsible for the signage? Is it the toll road authority for everything? Or does the state DOT do the signs on the free portion of the interchange? Or does each individual road vary?
Depends on what the jurisdiction is. That stuff that is maintained by the DOT would have DOT signs, and the stuff maintained by the toll authority would be signed by the toll authority (barring some maintenance agreement that changes things, such as NYCDOT doing some sign replacements on the freeways down there, even those are owned by NYSDOT). With the Thruway, the jurisdiction changes part way between the toll booth and where the ramp meets the free road.