What does Buddhism say about the existence of a self?

Anatta and Sunyata doctrines from the Tripitaka and later Mahayana/Parjnaparimata sutras both have mentioned "not-self" or "empty of self" doctrines. I am still a bit confused, though, even after extensive reading and practice. Does Buddhism, in general, ever deny the fundamental existence of a self...or does it simply state to not identify with it? And if the "not-self" or "emptiness of inherent existence" doctrines stress non-identification with the aggregates (name and form)...then who would be the one or the "I" doing the non-identification? Would the aggregates not be identifying with themselves if there was no actual "I?" Or would there be someone/something deeper than the aggregates? Thank you to all~.