Recently, the present authors proposed a model describing fullerene growth in carbon vapor for which the diffusion equation is assumed outside the fullerene and a family of possible Stefan conditions describe the growing fullerene surface. Here we consider a related model, but with the additional assumption that the fullerene surface atomic density is constant throughout the growth process, which is justified by experimental data. We show that this constraint on the fullerene lattice structure limits the solution to one possible Stefan condition. The proposed model may be extended to any nanostructure with constant atomic surface density. �� (2012) Trans Tech Publications, Switzerland.