Re: what does a plane autopilot do?
(in the early days of aircraft autopilots, mid-air collisions did happen as the planes were programmed to take the same routes)
You may be thinking of the habit of following railroad tracks, which resulted in at least one head-on collision before the convention to keep the track to the left of the airplane was established.
Most mid-air collisions between civil aircraft likely to have been using autopilot at that moment
have been ATC errors (like wrong flightlevel assigned) or navigational (craft is outside airlane, wrong altitude set, etc.). Not counting collisions between two or more military planes most mid-air collisions have been either between a civil airliner on autopilot and a military or recreational aircraft.