Fullerenes are lowest energy structures for gas phase all-carbon particles for a range of sizes, but graphite remains the lowest energy allotrope of bulk carbon. This implies that the lowest energy structure changes nature from fullerenes to graphite or graphene at some size and therefore, in turn, implies a limit on the size of free fullerenes as ground state structures. We calculate this largest stable single shell fullerene to be of size N = 1 × 10⁴, using the AIREBO effective potential. Above this size fullerene onions are more stable, with an energy per atom that approaches graphite structures. Onions and graphite have very similar ground state energies, raising the intriguing possibility that fullerene onions could be the lowest free energy states of large carbon particles in some temperature range.