Abstract One of the outstanding questions about synthesis of single-walled carbon nanotubes is what is the role and mechanism of carbon diffusion during chemical vapor deposition synthesis. Examination of individual trajectories of all carbon atoms in reactive molecular dynamics simulated growth of single-walled carbon nanotubes on supported nanoparticles identifies carbon atoms involved in surface diffusion, bulk diffusion, and potential carbide formation. We show that transitions between induction, nucleation, and growth are denoted by saturation of the nanoparticle and by changes in the catalytic regime. It is found that nucleation and dissolution may occur simultaneously, with pre-saturation nucleation driven by the low-energy barrier for surface diffusion. It is concluded that for carbon-philic catalysts, induction and nucleation periods are usually governed by bulk diffusion, while the growth period is dominated by surface diffusion. Surface diffusion control during growth is in agreement with successful nanotube growth on metals such as copper and gold, which do not dissolve carbon. In the range studied, C solubility decreases with particle size, and the Ni/C ratios found coincide with stoichiometries of known Ni carbides.