Generally speaking, each Diocesan Bishop regularly submits a list of priests to the Papal Nuncio. In some cases, this list is submitted on the Province level ( Archdiocese and suffergan diocese)
The Papal Nuncio will gather additional information on the potential canidates and submit this information to the Holy See, along with their recommendations.
As need arises, the Holy See will select canidates of of this information, and whatever other sources the Holy See deemes appropriate.
The Holy See will, of course, appoint the man they feel most appropriate to the role based on their own judgement.
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