A method for co-extruding multiple polymer plastic materials for injection through a gate region into a mold cavity to produce a molded article, the mold cavity having inner and outer annular flow boundaries and the molded article having inner and outer article walls, the method comprising: co-extrusively flowing streams of polymer plastic materials, including: inner and outer streams of plastic material that are to serve as covering wall inner and outer layers, respectively, of plastic material in the resulting molded article, and at least one interior stream of plastic material that is to serve as an interior core of plastic material encased within the inner and outer layers in the resulting molded article; forcing the flowing streams to flow along concentric annular flow paths within and along a longitudinally extending tubular extruder nozzle to the gate region; characterized in that the method further comprises: adjusting the flowing streams initially to cause an initial portion of the interior stream to start to flow at a region of substantially zero velocity gradient in the transverse flow velocity profile of the extrusion; and after the substantially zero velocity gradient flow of the interior stream has started, subsequently varying the relative volumetric flow ratio of the inner stream to the outer stream in order to offset the interior stream from the zero velocity gradient and to consequently shift the interior stream closer to the inner annular flow boundary or the outer annular flow boundary such that, in the resulting molded article, a major portion of the interior core is closer to the inner article wall or the outer article wall than to the other. co-extrusively flowing streams of polymer plastic materials, including: inner and outer streams of plastic material that are to serve as covering wall inner and outer layers, respectively, of plastic material in the resulting molded article, and at least one interior stream of plastic material that is to serve as an interior core of plastic material encased within the inner and outer layers in the resulting molded article; inner and outer streams of plastic material that are to serve as covering wall inner and outer layers, respectively, of plastic material in the resulting molded article, and at least one interior stream of plastic material that is to serve as an interior core of plastic material encased within the inner and outer layers in the resulting molded article; forcing the flowing streams to flow along concentric annular flow paths within and along a longitudinally extending tubular extruder nozzle to the gate region; adjusting the flowing streams initially to cause an initial portion of the interior stream to start to flow at a region of substantially zero velocity gradient in the transverse flow velocity profile of the extrusion; and after the substantially zero velocity gradient flow of the interior stream has started, subsequently varying the relative volumetric flow ratio of the inner stream to the outer stream in order to offset the interior stream from the zero velocity gradient and to consequently shift the interior stream closer to the inner annular flow boundary or the outer annular flow boundary such that, in the resulting molded article, a major portion of the interior core is closer to the inner article wall or the outer article wall than to the other.