An assembly for realizing in continuous covering jackets of book elements of different dimensions starting from a film wrapped up in a coil. The assembly includes a mechanism for cutting the film unrolling from the coil for realizing pieces of the film; a first folding device of a first end of the pieces; a second folding device of a second end of the pieces; a control and command unit and a longitudinal welder suitable for both superiorly and inferiorly closing folded pockets and for regulating the height of the cover itself by trimming the parts in excess.