An apparatus for producing polymeric nanofibers utilizes a meltblown spinneret die having spin holes formed by grooves in plate(s) surface(s) of plate(s) where polymer exits at the plate(s) edge(s). The grooves are smaller than 0.005″ wide×0.004″ deep and have an L/D at least as large as 20:1. Flow rates of polymer through the apparatus are very low, on the order of 0.01 ghm or less. A meltblown fabric having fibers mostly less than 0.5 microns in diameter is produced.