Who registers
The provider registers itself and its high-risk system from Annex III in the EU database before it is placed on the market or put into service [1]. A provider that considers its system to fall under the exception in Article 6(3) also registers it [2].
Deployers
Deployers register only if they are public authorities or Union institutions, bodies, offices or agencies, or act on their behalf [3] [4]. If you have a high-risk system developed yourself and use it under your own name [7], or you become a provider under Article 25 [6], you have the provider's registration duty [1].
From when
Registration attaches to high-risk systems from Annex III, and those are treated as high-risk from 2 December 2027 [5].