Carbon materials having carbon aggregates, where the aggregates include carbon nanoparticles and no seed particles, are disclosed. In various embodiments, the nanoparticles include graphene, optionally with multi-walled spherical fullerenes and/or another carbon allotrope. In various embodiments, the nanoparticles and aggregates have different combinations of: a Raman spectrum with a 2D-mode peak and a G-mode peak, and a 2D/G intensity ratio greater than 0.5, a low concentration of elemental impurities, a high Brunauer-Emmett and Teller (BET) surface area, a large particle size, and/or a high electrical conductivity. Methods are provided to produce the carbon materials.