The condensational growth of aerosol particles initially formed by a nucleation process is considered within the theoretical approach proposed by Lushnikov & Kulmala, (1995) (referred hereafter to as LK) for treating source enhanced condensation processes. The molecules of condensing vapor are assumed to be able to form dimers, trimers etc. which evaporate very quickly if their masses are below certain value g = G, otherwise they are stable against evaporation and grow by joining the vapor molecules by one. The expression for the nucleation rate is derived. Special attention is given to the case G = 3. The probability for the dimer fragmentation as the function of temperature is found analytically.