A coadjutor bishop (or bishop coadjutor) is a bishop in the Roman Catholic or Anglican churches who is designated to assist the diocesan bishop in the administration of the diocese, almost as co-bishop of the diocese. The coadjutor (literally, "co-assister" in Latin) is a bishop himself and is given authority even beyond that ordinarily given to the vicar-general (although a coadjutor is also appointed a vicar-general), making him co-ruler of the diocese in all but ceremonial precedence. In modern times, the coadjutor automatically succeeds the current bishop of a diocese upon the latter's retirement, removal or death.
Roman Catholic Church 
In the Roman Catholic Church, a coadjutor bishop is an immediate collaborator of the diocesan bishop, similar to an auxiliary bishop. Unlike auxiliary bishops, coadjutors are given the automatic right of succession to the episcopal see, meaning that when the diocesan bishop dies, retires, resigns, or is reassigned, the coadjutor automatically becomes the next bishop of the local Church (diocese). Until then, the diocesan bishop appoints the coadjutor to act as vicar general.
In modern church practice, the appointment of a coadjutor is usually done in cases where a diocesan bishop feels that he will not be able to continue much longer for health reasons or because he is nearing retirement age. In these cases the Pope will sometimes assign a coadjutor in order to give him time to become familiar with the diocese that he will eventually take over. Such was the case when Bishop Dennis Marion Schnurr of the Roman Catholic Diocese of Duluth, Minnesota, was named Coadjutor Archbishop of the Roman Catholic Archdiocese of Cincinnati, Ohio, in 2008 to succeed the aging Archbishop Daniel Edward Pilarczyk in 2009; Pilarczyk had been serving since the early 1980s. Another example is the appointment of San Antonio Archbishop Jose Gomez to succeed Cardinal Roger Mahony as Archbishop of Los Angeles when Mahony retired at 75 in February 2011.
At times, the appointment of a coadjutor is used to discreetly remove a diocesan bishop who has become involved in scandal or other problems and replace him with another man. An example of this occurred in the Archdiocese of Dubuque in the 1940s, when then Archbishop Francis Beckman involved the archdiocese in what turned out to be a dubious mining scheme. When the scheme fell apart and the man behind the scam was arrested, the fallout resulted in serious financial problems for Archbishop Beckman and the archdiocese. Because of all of Beckman's problems, Bishop Henry Rohlman of Davenport, Iowa, was appointed Coadjutor Archbishop of Dubuque. While Beckman was allowed to retain the office of Archbishop, it was made clear to him by the Holy See that the actual power rested with Rohlman. Beckman soon retired and left Dubuque. Another example would be that of Cardinal Pedro Segura y Sáenz, whose responsibilities as Archbishop of Seville were given to his Coadjutor Archbishop José Bueno y Monreal.
Prior to the reform of the Code of Canon Law in 1983, a distinction was made between coadjutor bishops cum jure succesionis and those without – that is, some coadjutors were appointed with the automatic right of succession, and others without such a right (the latter were usually appointed for archbishops with particularly large dioceses who also held other important posts and to honor certain auxiliary bishops – for instance, Coadjutor Archbishop John Maguire assisted Cardinal Francis Spellman, who was simultaneously Archbishop of New York and also head of what later became the Archdiocese for the Military Services, USA, two of the largest archdioceses in the country).
Now, no coadjutor is appointed without the concomitant right of succession.
Anglican Communion 
In some provinces of the Anglican Communion, a bishop coadjutor (the form usually used) is a bishop elected or appointed to follow the current diocesan bishop upon the incumbent's death or retirement. For example, in the Episcopal Church in the United States of America, when a diocesan bishop announces his or her retirement, a special diocesan convention is held to elect a coadjutor. Usually the coadjutor serves with the incumbent for a short time before the latter's retirement, at which time the coadjutor becomes the diocesan bishop. Bishops coadjutor are also appointed in the Reformed Episcopal Church.