I used to fly for KRON the San Francisco NBC affiliate, (they are an independent news station now)----there is NO autopilot. Unless you are watching continuing coverage, they are not remaining in the hover all the time.
Back in the 90's we would all fly around in an orbit until our station wanted the "steady shot" to go live, at which point we would move into position and hover. We would all talk to each other and work out our own co-ordination and stay out of other peoples shot as best as possible. (The airspace over downtown San Francisco is not controlled by ATC).