The connection between Nietzsche and Rand is interesting.

Personally, I see Nietzsche as a ranting narcissist like Joseph Smith. Both were in love with their ideas and both managed to form a cult following.

It is interesting that Nietzsche saw himself as anti-authoritarian and his rantings became a favorite read of the National Socialists who saw themselves as Nietzsche uber-men driving by the will to power to become the worst authoritarians in history.

Youtube has a video where Rand claims that Objectivism is a fundamental rejection of Nietzsche and Schopenhauer.

Ayn Rand seems to face the problem of all philosophies in that reactionary philosophies always end up bearing an imprint of the thing the philosopher is reacting against.