§1. When the pastoral needs of a diocese suggest it, one or more auxiliary bishops are to be appointed at the request of the diocesan bishop. An auxiliary bishop does not possess the right of succession.
§2. In more serious circumstances, even of a personal nature, an auxiliary bishop provided with special faculties can be given to a diocesan bishop.
§3. If it appears more opportune to the Holy See, it can appoint ex officio a coadjutor bishop who also has special faculties. A coadjutor bishop possesses the right of succession.
Source: Code of Canon Law (Vatican.va)