A component assembly comprising a sheet metal part and a fastener element which has a flange part of larger diameter and a shaft part of smaller diameter which extends away from the flange part and merges at its end remote from the flange part into a cylindrical rivet section is characterized in that the fastener element is designed for use with sheet metal parts with thicknesses in the range of 3 mm and larger. With relatively thin sheet metal parts the sheet metal part has a smooth pierced cylindrical opening which has a diameter corresponding to the diameter of the shaft part, with the cylindrical rivet section being reshaped to a rivet bead which contacts the underside of the sheet metal part. With sheet metal parts of medium thickness the sheet metal part has a stepped hole with the hole region of larger diameter receiving the rivet bead. For relatively thick sheet metal parts the sheet metal part has a conical pierced hole and the cylindrical rivet section is reshaped to a conical rivet bead which is wedged in the conically diverging hole.