(57) The end device comprises: a tool carrier (30), an operative station (11), a gauge (5) to maximize the distance from the contour line of the tile (0) to the pressure points, as well as the distance from the small roller (34) or fulcrum (f) to the push-operable scoring and cutting disc-like tool (3) or scoring weight arm which is of about 30 mm. Such fulcrum (f) engaging the bottom of the guide (2), which is placed parallel over base (1) 45 mm beyond the reaction apex (7)), The power arm of the lever is 36 cm long. At parity of power arm, the weight arm is mm 90 long, whereby the pressers (4, 4') may operate at 100 mm far from the upright (10) or at least 22 mm from the contour line (0') and 32 mm inside the corner (0"). An adjuster means (38) limits the excursion of the pressers (4, 4') avoiding that the exceeding excursion thereof operates again accidentally on any of the already cut sections of the tile.