A nanoparticle or agglomerate which contains connected multi-walled spherical fullerenes coated in layers of graphite. In different embodiments, the nanoparticles and agglomerates have different combinations of: a high mass fraction compared to other carbon allotropes present, a low concentration of defects, a low concentration of elemental impurities, a high Brunauer, Emmett and Teller (BET) specific surface area, and/or a high electrical conductivity. Methods are provided to produce the nanoparticles and agglomerates at a high production rate without using catalysts.