If one wanted to, how large part of the flight could a modern commercial airliner do completely on its own? That is, if the pilot only was allowed to set things up and then leave the cockpit, from where (taxiing, take off, et cetera) and for how long would the airplane be able to handle things itself before things went out of hands?
This should apply to the most advanced modern airliners. Older aircraft may not have all of the same automation available. The autopilot can take care of most tasks between takeoff and landing.
The pilots have to take care of starting the airplane. This includes turning on electronics, bringing up the aircraft systems, and starting the engines.
Taxiing is pretty much on the pilot, there is no automatic taxi yet on commercial airliners.
Once the aircraft is lined up with the runway, the pilot can hit the TOGA (Takeoff/Go Around) button. The plane will automatically apply the right amount of thrust for takeoff. The pilot will then rotate the plane (lift the nose) at the rotation speed (calculated before the flight), and the plane lifts off. Shortly after that, the pilot will engage the autopilot.
If the autopilot is set up to follow GPS waypoints and proper altitudes, it will be able to take care of the climb, cruise, and descent portions of the flight. The autopilot can follow the best speeds and fly through each waypoint in the flight plan.
Once the aircraft is approaching the runway, the pilot will tune the proper ILS frequency for the runway into the navigation radio. They will then engage the Approach mode, which captures the localizer (lateral navigation left/right to align with the runway) and glideslope (veritical navigation up/down to have the proper approach path). The pilot then needs to deploy the flaps and landing gear as the plane slows down for landing.
In the lowest visibility conditions, the plane is capable of the approach and touchdown on the runway all by itself. The pilot will then apply reverse thrust and brakes as needed to slow down.
Now that the plane is back on the ground, it is once again the pilot's job to exit the runway and taxi to the gate. Shutting down the engines and then the electronics will also be up to the pilot.
What is the autopilot still missing?
- Responding to ATC (readback clearances, change frequencies)
- Reacting to nearby traffic
- Following ATC instructions (climb/descend, turn, slow/accelerate)
- Reacting to emergencies or system failures
- Controlling lights, flaps, landing gear
This is of course a high level view and there is so much more that goes into the flights.
Also, keep in mind that we have the technology to do much more. It just hasn't made it into service for one reason or another (lack of development and testing, not seen as important, etc.). We have UAVs that are much more automated than this. However, they are still working on how to effectively avoid other aircraft.