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the Congregation for the Clergy handles dispensations from Holy Orders, and the Congregation for Cathoilc Education exercises jurisdiction over Catholic universities and faculties including those Eastern.
The CDF does have competence regarding the Eastern Churches. Note that there is a common faith which all Catholics hold, regardlesss of the existence of various theological traditions.
Pastor Bonus on Congregation for Oriental (Eastern) Churches:
Art 58 § 2. This however does not infringe on the proper and exclusive competence of the Congregations for the Doctrine of the Faith and for the Causes of Saints, of the Apostolic Penitentiary, the Supreme Tribunal of the Apostolic Signatura or the Tribunal of the Roman Rota, as well as of the Congregation for Divine Worship and the Discipline of the Sacraments for what pertains to dispensation from a marriage
ratum et non consummatum.
An example of CDF for the Eastern Churches is the *nihil obstat: *certification that a publication contains nothing contrary to faith or morals.
For the Congregation for the Clergy: it has competency over the dispensation of the obligations inherent to the sacred ordination of the diaconate and the presbyterate of the regular and diocesan clergy of
both the Latin and Oriental Churches, according to the letter of the Secretariat of State, no. 907 of June 21, 2005.
The Congregation for Cathoilc Education exercises jurisdiction over Catholic universities and faculties including those Eastern.
This dicastery has authority in three diverse sectors: over all seminaries (except those falling within the jurisdiction of the Congregations for the Evangelization of Peoples and for Oriental Churches) and houses of formation of religious and secular institutes; over all universities, faculties, institutes and higher schools of study, either ecclesial or civil dependent on ecclesial persons; over all schools and educational institutes depending on ecclesiastical authorities.
vatican.va/roman_curia/congregations/ccatheduc/documents/rc_con_ccatheduc_20051996_profile_en.html