At least on this the guidance http://ec.europa.eu/newsroom/article29/item-detail.cfm?item_id=612052 is quite clear:
"Article 26 concerns joint controllers and specifies that joint controllers shall determine their respective responsibilities for compliance with the GDPR25. This will include determining which party will have responsibility for complying with the obligations under Articles 33 and 34. WP29 recommends that the contractual arrangements between joint controllers include provisions that determine which controller will take the lead on, or be responsible for, compliance with the GDPR’s breach notification obligations. "
That will include both notifying the regulator, and if necessary the subject(s)
Interestingly my question arose from contemplating an agreement between controllers that a third party, who was either (a) not a controller at all or (b) a controller who did not in fact have access to the data would notify. If (a) I advised it was not on. If (b) I advised it could in theory work for notifying the regulator (but was a bad idea) but could not work for notifying the subjects as the controller would not actually know who they were and couldn't even be told without breaching confidentiality!
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