Chemically accurate ab initio Gaussian-3-type calculations of the C10H9 potential energy surface (PES) for rearrangements of the 9-H-fulvalenyl radical C5H5-C5H4 have been performed to investigate the formation mechanisms of polycyclic aromatic hydrocarbons (PAHs) originated from the recombination of two cyclopentadienyl radicals (c-C5H5) as well as from the intermolecular addition of cyclopentadienyl to cyclopentadiene (c-C5H6) under combustion and pyrolytic conditions. Statistical theory calculations have been applied to obtain high-pressure-limit thermal rate constants, followed by solving kinetic equations to evaluate relative product yields. At the high-pressure limit, naphthalene, fulvalene, and azulene have been shown as the reaction products in rearrangements of the 9-H-fulvatenyl radical, with relative yields depending on temperature. At low temperatures (T < 1000 K), naphthalene is predicted to be the major product (> 50%), whereas at higher temperatures the naphthalene yield rapidly decreases and the formation of fulvalene becomes dominant. At T > 1500 K, naphthalene and azulene are only minor products accounting for less than 10% of the total yield. The reactions involving cyclopentadienyl radicals and cyclopentadiene have thus been shown to give only a small contribution to the naphthalene production on the C10H9 PES at medium and high combustion temperatures. The high yields of fulvalene at these conditions indicate that cyclopentadienyl radical and cyclopentadiene more likely represent significant sources of cyclopentafused PAHs, which are possible fullerene precursors. Our results agree well with a low-temperature cyclopentadiene pyrolysis data, where naphthalene has been identified as the major reaction product together with indene. Azulene has been found to be only a minor product in 9-H-fulvalenyl radical rearrangements, with branching ratios of less than 5% at all studied temperatures. The production of naphthalene at low combustion temperatures (T < 1000 K) is governed by the spiran mechanism originally suggested by Melius el. al. At higher temperatures, the alternative C-C bond scission route, which proceeds via the formation of the cis-4-phenylbutadienyl radical, is competitive with the spiran pathway. The contributions of the previously suggested methylene walk pathway to the production of naphthalene have been calculated to be negligible at all studied temperatures.