A formation regime of fullerenes and carbon nanotubes in glow-discharge reactive plasmas is investigated in order to gain sharp insight into the relation between plasma characteristics and the generation processes of the fullerene families. The plasma is produced in a mixture of CH4 and a small fraction of H-2 by the radio-frequency (RF) discharge across an externally-applied magnetic field. The plasma is found to be apparently localized around the RF electrode under certain conditions determined by the magnetic field strength and reactive-gas pressure. In this case, it is demonstrated that fullerenes and carbon nanotubes are most effectively generated on the RF electrode, which is negatively self-biased, and exposed to a strong plasma-sheath drop. Our results indicate that the creation of radical species, such as hydrocarbon precursors, due to the local discharge around the RF electrode, the sheath acceleration of positively-charged particles such as carbon ions, and the abstraction of the hydrogen from hydrogenated-carbon species or clusters, are important in the nucleation, formation, and growth of the fullerene families.