What can cause motor to keep running shortly after key is turned off?

When I shut my key off there is a few seconds delay before the engine shuts down. When I try to start it up again it usually sputters a bit before it smoothes to an idle. I am guessing this is too much fuel in the throttle body. I read I am not supposed to try adn adjust the idle because its self controlled but am wondering if maybe its off time a little bit or what I can do to keep it running smoothly.