Apparatus to cover a filiform core with a silicone-based polymer material, comprising: - an extrusion station comprising a co-extrusion body suitable to receive the polymer material, a feeder body provided with a calibrating head in which the filiform core to be covered transits centrally, and an exit nozzle through which the filiform core exits from the co-extrusion body with the polymer material disposed at least partly around it, along an axis of extrusion, forming an extruded filiform article, said exit nozzle being provided with an exit aperture disposed so that said extrusion axis is substantially vertical; - a stabilization station, located downstream of said extrusion station; and - a collection unit to collect the extruded article, provided with drawing devices able to exert a controlled traction force on said article in order to guarantee at least that it advances toward said stabilization station in a substantially vertical direction, characterized in that said calibrating head is aligned along said axis of extrusion coaxial to said co-extrusion body at least in proximity to said exit nozzle, and defines with said exit nozzle a transit channel for the polymer material from the co-extrusion body toward the aperture, wherein said co-extrusion body and said feeder body are configured and disposed in such a way that the polymer material is disposed around the filiform core in correspondence with said outlet nozzle; and wherein said calibrating head is axially mobile in the direction of said extrusion axis and is associated with positioning means configured to move said calibrating head and position it at a desired height with respect to said exit nozzle and said aperture in order to modify the amplitude of said transit channel and consequently the quantity of polymer material deposited around said filiform core and the thickness of said extruded article. - an extrusion station comprising a co-extrusion body suitable to receive the polymer material, a feeder body provided with a calibrating head in which the filiform core to be covered transits centrally, and an exit nozzle through which the filiform core exits from the co-extrusion body with the polymer material disposed at least partly around it, along an axis of extrusion, forming an extruded filiform article, said exit nozzle being provided with an exit aperture disposed so that said extrusion axis is substantially vertical; - a stabilization station, located downstream of said extrusion station; and - a collection unit to collect the extruded article, provided with drawing devices able to exert a controlled traction force on said article in order to guarantee at least that it advances toward said stabilization station in a substantially vertical direction, wherein said co-extrusion body and said feeder body are configured and disposed in such a way that the polymer material is disposed around the filiform core in correspondence with said outlet nozzle; and wherein said calibrating head is axially mobile in the direction of said extrusion axis and is associated with positioning means configured to move said calibrating head and position it at a desired height with respect to said exit nozzle and said aperture in order to modify the amplitude of said transit channel and consequently the quantity of polymer material deposited around said filiform core and the thickness of said extruded article.