BMW Repair: radiator over flow and runs hot, blown head gasket, model engine

Question
my radiator over flows while the car is running then when I turn it off it all goes out then when I start the cat it over flows again and runs hot after about 20 miles and my fan only comes on with the air condition.

Answer
You have to understand that you haven't told me the year, model engine or country this car is in.

But based on the little information you have provided, it sounds like you may have a blown head gasket.  If so, hot pressurized compression gases go through the breached gasket, and force out the coolant.  The car overheats, because there is no coolant to take away the heat.

If this is the case, it is serious, and further driving can ruin the entire engine.