The territorial prelate is sometimes called a prelate nullius, from the Latin nullius dioeceseos, prelate "of no diocese," meaning the territory falls directly under the 'exempt' jurisdiction of the Holy See (Pope of Rome) and is not a diocese under a residing bishop.
The term is also used in a generic sense, and may then equally refer to an apostolic prefecture, an apostolic vicariate, a permanent apostolic administration (which are pre-diocesan, often missionary, or temporary), or a territorial abbacy (see there).
A territorial prelate exercises quasi-episcopal jurisdiction in a territory not comprised by any diocese. The origin of such prelates must necessarily be sought in the apostolic privileges, for only he whose authority is superior to that of bishops can grant an exemption from episcopal jurisdiction. Such exemption, therefore, comes only from the pope.
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. If they have not received episcopal consecration, such prelates may not confer holy orders. If not consecrated episcopally, they have not the power to exercise those functions of consecrating oils, etc., which are referred to the episcopal order only analogously.
Prelates nullius may take cognizance of matrimonial causes within the same limits as a bishop. 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. They may, even if priests only, confirm themselves by papal privilege as expressed in canon 883 No. 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.
These prelates may not, however, without special permission of the Holy See, convoke a synod or institute synodal examiners. Neither may they confer parochial benefices. 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.
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.
As a rule, territorial (and personal) prelates are consecrated as bishops, though not bishops of their diocese, as expressed by the title Bishop-prelate.
Most were/are missionaries, outside Europe (mainly Latin America and a few Asian countries) or in countries with a crushing Protestant majority (notably Lutheran Norway).
As of November 2020, there were 40, all Latin Church:
(probably quite incomplete; all Latin)