The rights of prelates nullius are quasi-episcopal, and these dignitaries are supposed to have any power that a bishop has, unless it is expressly denied to them by canon law.
They may dispense from the proclamation of matrimonial banns, grant faculties for hearing confessions and preaching, reserve certain cases to themselves, publish indulgences and jubilees, exercise full jurisdiction over the enclosure of nuns, and invite any bishop to confirm in their quasi-diocese.
1 CIC whenever they find it appropriate; however, even as local ordinaries they are in that case only extraordinary ministers of confirmation and should thus prefer to invite bishops if possible.
They are not allowed to grant indulgences, or absolve from the reserved cases and secret irregularities whose absolution is restricted to the pope ordinarily, but allowed to bishops by the Council of Trent, nor promote secular clerics to orders, nor grant dimissory letters for ordination, nor exercise jurisdiction over regulars as apostolic delegates.
[2] Prelates nullius are, however, bound to residence, to preach the Word of God, to offer Mass for their people, to make the visit ad limina to the Roman Curia, and in concurrence with the neighbouring bishop to perform a visitation of their quasi-diocese.