The term "coadjutor" (literally "co-assister" in Latin) is a title qualifier indicating that the holder shares the office with another person, with powers equal to the other in all but formal order of precedence.
In this latter sense it is expressly forbidden by the Council of Trent; nevertheless the Pope, for special causes, sometimes concedes it, the plenitude of his apostolic power enabling him legally to dispense with the law.
Since a cleric who enjoys a benefice cannot be deprived of it on account of old age or infirmity, it is fitting that he should have someone to assist him in the work.
canons only speak of parochial churches; and the Council of Trent orders the bishops, as delegates of the Holy See, to provide parish priests, who are ignorant but of good life, with coadjutors and vicars, and to assign these a sufficient share of the fruits of the benefice.
As regards benefices without cure of souls, it is not the custom to give these temporary coadjutors, as the end in view can be attained by other means.