Molecular-dynamics and total-energy calculations using a realistic three-body potential for carbon reveal the basic atomic processes by which single-shelled nanotubes can grow out of metal-carbide particles by the root growth mechanism. We find that nanometer-sized protrusions on the metal-particle surface lead to the nucleation of very narrow tubes. Wide bumps lead to a strained graphene sheet and no nanotube growth. The results also explain the absence of multishelled tubes in metal-catalyzed growth.