The energetics and kinetics of phenalene and phenalenyl growth reactions were studied theoretically. Rate constants of phenalene and phenalenyl H-abstraction and C2H2 addition to the formed radicals were evaluated through quantum-chemical and rate-theory calculations. The obtained values, assigned to all π radicals, were tested in deterministic and kinetic Monte Carlo simulations of aromatics growth under conditions of laminar premixed flames. Kekulé and non-Kekulé structures of the polycyclic aromatic hydrocarbons (PAHs) evolving in the stochastic simulations were identified by on-the-fly constrained optimization. The numerical results demonstrated an increased PAH growth and qualitatively reproduced experimental observations of Homann and co-workers of non-decaying PAH concentrations with nearly equal abundances of even and odd carbon-atom PAHs. The analysis revealed that the PAH growth proceeds via alternating and sterically diverse acetylene and methyl HACA additions. The rapid and diverse spreading in the PAH population supports a nucleation model as PAH dimerization, assisted by the non-equilibrium phenomena, forming planar aromatics first and then transitioning to the PAH-PAH stacking with size.