Molecular dynamic (MD) simulations of the Combined Condensation and Annealing (CCA) of free carbon atoms was used to investigate the statistical abundance and stability of neutral carbon nanostructures for a cluster size between 2 and 54 atoms. During these CCA MD-simulations carbon atoms are submitted to a condensation/heating phase, a CTR phase at a prescribed annealing temperature and a cooling phase. Numerical experiments showed that the determination of the statistical abundances requires at least 100 ns condensation/heating phase, 100 ns CTR phase at the annealing temperature and 100 ns cooling phase. The clusters obtained by CCA MD-simulations are dominated by linear structures for n=2-5, mono-ring for n=6-15, multi-ring structures for n=16-18, 2D graphene-like structure for sizes in the range n=19-29 and cage-like structure above n=30. Open cage structures are obtained at temperature around 2000 K, while closed cage structures dominate at 3000 K. For even larger temperature, i.e., 4000 K, the dominant structures are 2D and 3D multi-ring structures, 2D graphene-like structure remaining quite significant.