For those questioning the auto-trim on the airbus - this is a function of the FBW system.
On a conventional aeroplane (PA28 or 737) the pilot pitches up using the control column and manually trims the pressure off using the trim wheel or electric trim switch (same thing).
On the airbus this happens automatically. The pilot pitches the aeroplane up with sidestick inputs and the computer trims off the resulting "pressure" (you can still see the trim wheel rotating back during this process).
If the pilot applies sufficient back stick for a sufficient amount of time then the trim will wind fully back to the stop. This is what happened during the deceleration phase of the Perpignan Accident and almost certainly what happened during the Air France 447 tragedy.
In some conditions the auto-trim disconnects (abnormal attitude and direct law) and the trim setting and therefore wheel and stabiliser will remain in that final position until either
a) auto-trim is restored
or
b) the pilot moves the trim wheel manually!