The role of auxiliary bishops is indeed one that supports diocesan governance. Here's how:

Nature of the Office

• Auxiliary bishops are appointed to assist diocesan bishops when the pastoral needs of a diocese suggest it, such as a vast territory, a large population, or the special nature of the apostolate 1 2. They are appointed without the right of succession 3.
• A coadjutor bishop, on the other hand, is appointed with the right of succession and must always be named vicar general by the diocesan bishop 2 3.

Responsibilities and Duties

• Auxiliary bishops are granted the faculties necessary to make their work more effective while maintaining the unity of diocesan administration and the authority of the diocesan bishop 1.
• They assist the diocesan bishop in the entire governance of the diocese and take his place if he is absent or impeded 4.
• Both coadjutor and auxiliary bishops are obliged to reside in the diocese, similar to the diocesan bishop 5. They can only be absent for a brief time to fulfill duties outside the diocese or for vacation, which should not exceed one month 5.
• A diocesan bishop should not hesitate to ask for one or more auxiliaries if the good of souls demands it 3. Unless otherwise determined, the powers and faculties of auxiliary bishops do not cease when the office of the diocesan bishop ends 3.

Collaboration and Consultation

• A diocesan bishop, coadjutor, and auxiliary should consult one another on matters of major importance to foster the present and future good of the diocese 6. The diocesan bishop should consult the auxiliary bishops before others when considering cases of major importance, especially those of a pastoral nature 6.
• Coadjutor and auxiliary bishops are called to share in the solicitude of the diocesan bishop and should exercise their duties in harmony with him in effort and intention 6. They should show respect and reverence for the diocesan bishop, who, in turn, should have fraternal love and esteem for them 1.

In summary, auxiliary bishops play a crucial role in supporting diocesan governance by assisting the diocesan bishop in various pastoral and administrative duties, ensuring the well-being of the diocese and its faithful 1 4 6.