cross section of the core where the application of adhesive takes place for the application of the adhesive a disc 42 is provided which is able to rotate by a continuous motion with a peripheral speed which may be less than the core advancement speed at the position a3 in any case the relative speeds give rise to a mutual rubbing of the disc periphery and the core lower zone so as to allow the disc to effectively apply the adhesive to the core in a uniform way and in relatively limited amounts disc 42 is arranged to dip into an adhesive container 44 which can be suitably stirred and kept at a desired level to make sure that disc 42 picks up a predetermined amount of adhesive at every revolution scraper means may also be provided to ensure the distribution of a constant amount of adhesive clearly with such an arrangement the adhesive is applied because of the movement of the core by belt 12 along a lower longitudinal portion with respect to the location of the core between support 9 and the upper active position of belt 12 the core that has received the adhesive reaches the rewinder r and is directly inserted in axial direction see arrow f12 with a continuation of the movement allowing same core to be timely positioned and thus in condition to be inserted between the cylinders of the winding system of the rewinder fig6 and 7 show schematically a feasible embodiment of the system for the winding of the paper web intended to form a log roll on the core as these rewinders are of various and known type only the main elements will be herein.