Isaac - the definition is that you must have passed it to a player with the intention for him (or her) to score. The amount of dribbles is irrelevant.
If Reesy got a defensive board, threw an outlet to Willie who was at the half way line, who dribble down for a dunk, that's be an assist to Reesy, because he passed to Willie with the intention for him to score. Make sense?
It is NOT as assist if it is deemed that the scorer created the score himself. IE - if Willie then had to weave through all 5 defenders and had pulled 4 crossover moves before he scored in the situation above, it would not be an assist.
RE: Screens. I don't think they should count as an assist. If it were like Ice Hockey, where they award 2 assists on some scores, then I would say a screener could be rewarded. However, in basketball, I think leaving it at 1 possible assist per basket scored is the best way to go :-).
Perhaps we could get clarification on what I've stated above from "Shutup!" who appears to be a stats person.....