A substantially vertical separating column of a waste-product treatment apparatus has a cylindrical body with holes in a lateral surface, inferiorly of a waste-product supply opening. A bladed shaft rotates coaxially inside the cylindrical body. A first discharge mouth in an upper part of the cylindrical body expels a first waste-product recycling fraction, the fraction separated and transported upwards by the bladed shaft. A dilution group along the separating column supplies dilution liquid internally of the cylindrical body. A second discharge mouth in the lower part of the cylindrical body evacuates a second recycling fraction. A discharge conduit and a screw extend parallel to a tangent to the cylindrical body, facilitating extraction of the first recycling fraction to the discharge conduit. The bladed shaft comprises a rotor and, in proximity of the upper end, a plate fixed to a lateral rotor surface and arranged radially.