This study quantitatively tests the proposed model of induced nucleati
on of carbonaceous grains in carbon-rich red giant stars. Induced nucl
eation is the process of grain growth initiated by the presence of rea
ctive surfaces provided by seed particles. The numerical study was per
formed using a detailed chemical kinetic model of carbon deposition, g
rain coagulation, and homogeneous nucleation of polycyclic aromatic hy
drocarbons (PAHs). The model uses a method of moments to keep track of
developing grain population in the forming dust shell. We test the ef
ficiency of grain formation for large ranges of dust shell parameters
typical for carbon stars. Our model is capable of producing a range of
optically thick and thin dust shells in carbon stars. Results are in
accord with IRAS spectral classes of carbon stars. The resulting compo
site grains produced are consistent with those recently found in ancie
nt meteorites. This model also provides a realistic explanation for hi
gh abundances of polycyclic aromatic hydrocarbons (PAHs) in the inters
tellar medium and some planetary nebulae.