The mechanisms of carbon sticking reactions to C36 and C–C80 fullerenes were investigated with molecular dynamics simulations (MD) using the Second-generation Reactive Empirical Bond Order (SREBO) and Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potentials that were specifically optimized for carbon-carbon interactions. Results showed the existence of three possible sticking configurations where the projectile atom can stick either to one, two or three atoms of the target fullerene. They also showed that although the two potentials give similar magnitudes for the sticking cross-sections, they yield fairly different results as far as sticking mechanisms and configurations at thermal collision-energies, i.e., in the range 0.05–0.5 eV, are concerned. While AIREBO, that takes into account the long-range Lennard-Jones interaction, essentially results in a surface-sticking configuration with a single atom of the target fullerene, SREBO potential yields both surface- and two neighbors-sticking (2N-sticking) configurations. The fullerene structure is preserved in the last configuration while it can be recovered by a 2000 K annealing in the former configuration. Results obtained with SREBO eventually showed larger sticking probabilities for C36 as compared with C80. In spite of this, the sticking cross-sections obtained for C80 are similar to or even larger than those obtained for C36 due to the larger size of C80 that compensates for its smaller sticking probabilities.