A device for coating a printing substrate, printed or to be printed with one or more copies, with a coating medium (06; 06'), in particular a varnish or a primer, said device comprising - a roller - and a feed system for supplying the roller with coating medium (06, 06'), which system cooperates with the roller, in the region of at least one contact zone on the periphery of said roller, to apply coating medium (06; 06') that will be applied to the printing substrate to the lateral surface of the roller in a continuous layer over an application width, - a removal device assigned to the roller and having removal elements, which are controllable separately via a control device, and by means of which coating medium (06; 06') applied previously by the feed system to the lateral surface, in a continuous layer over the application width, can be removed again from the lateral surface selectively, i.e. in one or more sections of partial width relative to the application width, in synchronization with the press phase position and/or printing substrate phase position for defined and/or definable phase lengths (l), prior to the transfer downstream, characterized in that - the roller, as a form roller, can be brought into rolling contact, in the region of a tangency zone, with the printing substrate to be coated, in order to coat said printing substrate on the side thereof that faces the form roller, - the coating medium (06; 06') that has been applied by the feed system to the lateral surface in a continuous layer over the application width can be removed selectively prior to the downstream transfer of said coating medium to the printing substrate, - in that the removal device, as viewed in the axial direction of the form roller, has a plurality of removal elements, which can be activated and deactivated mechanically independently of one another by respective actuators, in particular can be engaged against and disengaged from the lateral surface of the form roller in the circumferential region between the sole or the last contact zone with the feed system in the operational direction of rotation and the tangency zone with the printing substrate, wherein as the removal device, a doctor blade device is provided, which is arranged on the periphery of the form roller, offset from the contact zone with the sole or last feed system, and/or which comprises as removal elements at least ten doctor blades, which can be engaged independently of one another against the lateral surface in tracks that are offset from one another axially. - a roller - and a feed system for supplying the roller with coating medium (06, 06'), which system cooperates with the roller, in the region of at least one contact zone on the periphery of said roller, to apply coating medium (06; 06') that will be applied to the printing substrate to the lateral surface of the roller in a continuous layer over an application width, - a removal device assigned to the roller and having removal elements, which are controllable separately via a control device, and by means of which coating medium (06; 06') applied previously by the feed system to the lateral surface, in a continuous layer over the application width, can be removed again from the lateral surface selectively, i.e. in one or more sections of partial width relative to the application width, in synchronization with the press phase position and/or printing substrate phase position for defined and/or definable phase lengths (l), prior to the transfer downstream, - the roller, as a form roller, can be brought into rolling contact, in the region of a tangency zone, with the printing substrate to be coated, in order to coat said printing substrate on the side thereof that faces the form roller, - the coating medium (06; 06') that has been applied by the feed system to the lateral surface in a continuous layer over the application width can be removed selectively prior to the downstream transfer of said coating medium to the printing substrate, - in that the removal device, as viewed in the axial direction of the form roller, has a plurality of removal elements, which can be activated and deactivated mechanically independently of one another by respective actuators, in particular can be engaged against and disengaged from the lateral surface of the form roller in the circumferential region between the sole or the last contact zone with the feed system in the operational direction of rotation and the tangency zone with the printing substrate, wherein as the removal device, a doctor blade device is provided, which is arranged on the periphery of the form roller, offset from the contact zone with the sole or last feed system, and/or which comprises as removal elements at least ten doctor blades, which can be engaged independently of one another against the lateral surface in tracks that are offset from one another axially.