1) Do private airfields even exist anymore in the U.S.? (Google searches haven't really brought up much useful information on this one. My Google-fu is, shockingly enough, weak.)
2) What exactly is meant by "private"? Does it mean (as one would assume) that the owner of the property controls who gets to land and take off there? Is it basically understood that most private airfields are open to the public as long as they pay any requesite fees, etc?
3) What special regulations are the owners subject to?
Basically, I want an eccentric billionaire to own his own planes, airfield, etc. However, he doesn't like to share it with others. He also occasionally flies illegal passengers around under the government's nose - how likely is this scenario? (Bribes could certainly enter the equation, if need be.)