When is an aircraft considered dispatched? When is an aircraft considered to be dispatched?
Before an aircraft is dispatched certain pieces of equipment must be operational on an aircraft.  If some equipment is found to be inoperative, a determination can be made of whether or not to dispatch based on the information found in the MEL or CDL.
After an aircraft has been dispatched, disposition of inoperative equipment would follow the guidance inside the AFM.
Simply put, at what point does the dispatcher / crew switch over from relying on the MEL / CDL to the AFM for guidance?  The pilot in command has the final authority to takeoff so I am not asking about equipment that are significant to the operation of the airplane.
I am interested in both FAA Part 121 airline operations, Part 135 charter operations and Part 91 flights.
Thanks
Technically, before the aircraft is dispatched / released, everything can be inoperative.
However, most everything needs to be in working order to be dispatched / released, with exceptions as per the MEL / CDL.
MEL / CDL procedures are followed until the takeoff is commenced.
If an item is discovered to be missing or inoperative,
A) prior to door close
B) after door closed but prior to block out
C) after block out but prior to flight
there are specific MEL procedures to follow in each of those three scenarios.
Taking the runway and setting takeoff thrust / power is the act of commencing a takeoff.
After that point, equipment failures are treated as an in flight emergency, and flight crew follow QRH / AFM guidance. At that point the MEL no longer applies.
Applicable US FARs for Airline ops:
121.687 Dispatch Release - Flag or Domestic Operations
121.689 Flight Release - Supplemental Operations
135 has a similar regulation.
91k (fractional) does as well.
Plain Jane 91 owners/operators/pilots don't normally operate with an MEL. If they do, they have a letter of authorization with the FAA.