A line for the production of covered cardboard boxes, comprising: - a conveyor unit including a belt, which is movable to transport a plurality of covering blanks from a loading position to an unloading position, and a conveyor actuator connected to the belt to drive it intermittently in a sequence of movements and stops, started at respective movement instants alternated with corresponding stops; - a feed unit configured to feed the covering blanks individually to the conveyor unit at the loading position, in a sequence of feed instants corresponding to the sequence of movements; - an erecting machine configured to receive the cardboard box blanks and to fold them to form corresponding boxes; - a positioner configured to receive the boxes from the erecting machine and to position them individually in alignment on corresponding covering blanks disposed on the belt of the conveyor unit, at a coupling position interposed between the loading position and the unloading position; - a gluer configured to spread glue on one face of the covering blanks which will come into contact with a corresponding surface of the boxes to be covered; - a covering machine configured to receive the boxes coupled to the respective covering blanks from the conveyor unit at the unloading position and to fold each covering blank into contact with the respective box in such a way as to cover it, characterized in that it comprises a control unit, connected to the feed unit, to adjustably set a phase displacement (s) of the feed instants relative to the corresponding movement instants of the belt, wherein the control unit is programmed to receive format data, representing a format of the covering blanks, and to set working data as a function of the format data, wherein the working data are representative of the sequence of movements and stops of the belt and/or of the sequence of feed instants. - a conveyor unit including a belt, which is movable to transport a plurality of covering blanks from a loading position to an unloading position, and a conveyor actuator connected to the belt to drive it intermittently in a sequence of movements and stops, started at respective movement instants alternated with corresponding stops; - a feed unit configured to feed the covering blanks individually to the conveyor unit at the loading position, in a sequence of feed instants corresponding to the sequence of movements; - an erecting machine configured to receive the cardboard box blanks and to fold them to form corresponding boxes; - a positioner configured to receive the boxes from the erecting machine and to position them individually in alignment on corresponding covering blanks disposed on the belt of the conveyor unit, at a coupling position interposed between the loading position and the unloading position; - a gluer configured to spread glue on one face of the covering blanks which will come into contact with a corresponding surface of the boxes to be covered; - a covering machine configured to receive the boxes coupled to the respective covering blanks from the conveyor unit at the unloading position and to fold each covering blank into contact with the respective box in such a way as to cover it,