The static structural properties and the relative stability of fullerene molecules decorated with one, two, and three Ta atoms at different exohedral sites are investigated via first-principles calculations. We find that the most stable clusters are likely to be those in which a Ta atom is at a site of high electron density, such as the hexagon-hexagon double bond of the fullerene molecule, and if the Ta atoms cluster together on the surface of the cage. Dynamical simulations of the C₆₀Ta₃ system are performed via Car-Parrinello molecular dynamics, and they show that the Ta atoms on the surface of the fullerene are affected by a rather high mobility, similar to the surface diffusion of a physisorbed species. Though a Ta dimer is formed at relatively low temperatures, the C₆₀Ta₃ cluster is dynamically stable up to a temperature of ~1000 K, ruling out purely thermal heating as a major factor responsible for any fragmentation process at least on time scales of a few picoseconds.