BMW Repair: Car unlocking itself and windows opening, antenna amplifier, window antenna

Question
Hi, I have a BMW 3 series 316i SE 2003 that I purchased second hand in April this year. The fault has now occurred twice, both times the car was locked via the remote fob, all windows wound up closed and had been left like this for several hours(the second time was overnight). On returning to the car the central locking was open and all four windows were wound down varying amounts, all of them at least half way down.  

Answer
Mark, does this happen when the car is in the same place? You basically have four components of the convenience open function that as you decribe has been activated when you reach your car. The Remote Key, Rear Window (integrated antenna), Antenna Amplifier, and the Body controller (the General Module). You can rule out the window as the cause if the convenience open function works (hold unlock button on remote and windows and sunroof opens). Make sure your unlock button is not being depressed in your pocket or hand bag. Make sure you don't have another remote key in the car. Try using a different remote key and see if the same thing happens. That will either prove or eliminate the keys from the equation. Next I would try swapping or replacing the antenna amplifier that boosts the window antenna signal and sends it to the General Module. It is located in the Left rear C-pillar next to the rear window in U.S. model cars. If that Doesn't work then try replacing the GM. The GM has to be coded by the dealer and is located behind the glove box in the module carrier. You also could unplug the antenna amplifier to narrow down the problem to just the GM. You can also have the car and key memory set to disable the convenience open feature on the dealers coding machine if you never use the feature. So you have some options.
-Evan