Recital 128

(128) The provisions on the lead supervisory authority and the comprehensive cooperation mechanism should not apply where processing is carried out in the public interest by public authorities or private entities; in such cases, the only supervisory authority competent to exercise the powers conferred under this Regulation should be the supervisory authority of the Member State in which the public authority or private entity has an organisational unit.

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Recital 128 of the preamble to the GDPR | ODO 24