Can. 406 §1. The diocesan bishop is to appoint a coadjutor bishop and the auxiliary bishop as vicar general.
§2. a diocesan bishop is to appoint his auxiliary or auxiliaries as vicars general or at least as episcopal vicars, dependent only on his authority or that of the vicar general.
Can. 475 §1. In each diocese the diocesan bishop must appoint a vicar general who is provided with ordinary power according to the norm of the following canons.
Can. 479 §1. By virtue of office, the vicar general has the executive power over the whole diocese which belongs to the diocesan bishop by law, namely, the power to place all administrative acts except those, however, which the bishop has reserved to himself or which require a special mandate of the bishop by law.
§2. By the law itself an episcopal vicar has the same power mentioned in §1 but only over the specific part of the territory or the type of affairs or the faithful of a specific rite or group for which he was appointed, except those cases which the bishop has reserved to himself or to a vicar general or which require a special mandate of the bishop by law.
Can. 480 A vicar general and an episcopal vicar must report to the diocesan bishop concerning the more important affairs which are to be handled or have been handled, and they are never to act contrary to the intention and mind of the diocesan bishop.
Can. 883 The following possess the faculty of administering confirmation by the law itself:
1/ within the boundaries of their jurisdiction, those who are equivalent in law to a diocesan bishop
So, according to these canons, a coadjutor bishop is to be made vicar general, and an auxiliary bishop is to be at least episcopal vicar. Both the vicar general and the episcopal vicar have ordinary power in the diocese (although, over what? I’m not precisely sure), but they must report to the Ordinary bishop in important matters. It is not clear to me whether an auxiliary bishop, by virtue of his office of episcopal vicar and his episcopal dignity has the authority to make confirmations without (but not against) the permission of the Ordinary.