A method of applying protective sheeting of polymer material to a pipeline, such as on a J-lay rig, includes the steps of driving a carriage along an annular path about the pipeline; extruding and simultaneously winding the protective sheeting about the pipeline via an end extrusion die fitted to the carriage; compressing the protective sheeting on the pipeline, directly downstream from the end extrusion die, so the protective sheeting adheres to the pipeline; and controlling the drive, extrusion, and compression steps so that the time lapse between expulsion of a cross section of protective sheeting from the end extrusion die and compression of the same cross section of protective sheeting is less than one second.