This paper reports a molten salt electrolytic method for the economical production of carbon nanotubes/particles. The method converts a normal graphite cathode in a bath of molten LiCl, NaCl or KC1 into carbon nanotubes and other nano-particles. The cathode erosion observed after electrolysis, together with cyclic voltammetry, indicates that the conversion must have resulted from the graphite intercalation of the alkali metal that is formed at the cathode during electrolysis. In addition, the electrolytic carbon nanotubes and particles are found to be partially filled with a graphite-non-wetting material that cannot result from the known capillary effect. Logic suggests that the filled material is the cathodically formed alkali metal and therefore argues strongly that the graphite intercalation of alkali metals plays an important role in the formation of the electrolytic carbon nanotubes. An intercalation mechanism for the graphite-nanotube conversion is proposed.