After I fill up the gas tank, my car turns over, but then the engine stops. Why?

I fill up the gas tank, the fuller, the worse, then turn the engine over (turn the
key "on").  The rap meter reads normal for a split second, 2000/3000 idling in
"p" at the gas station.
Then the rpms sputters (within a few seconds), and goes to 0, and the engine
stops.  If I wait a bit, and try the whole thing over again, it gets a little better,
aka the sputtering, and stopping lasts a minute or two instead of seconds.
If I put the car in"d," the rpms immediately go to 0.  If I hit the gas pedal while
the car is in "p," or "d," the rpms stay high, and I can drive.
The biggest problem is getting out of the gas station spot, to the road.  I have
to have the car in "d," and tap the brakes.  Then my car stalls half way out into
the street, and I have to turn the car off, turn it on, put it in "d," and hit the gas
harder than normal, and semi-peel out of the gas station.
After driving for a bit like this the whole problem goes away, until I have to gas
it up again.