Analytical solutions to the steady-state kinetic coagulation equation, including sources, are presented for the case in which the collection kernel is of the form K = K0uβvβ, where K0 and β am constants (0 ≤ β < 1), and u and v represent aerosol particle volumes. Particle sources are represented by gamma distributions. The solutions look like modulated power law spectra, and rapidly approach their asymptotic power law form with increasing size. For, β = 0 the solution is equivalent to Friedlander's quasi-stationary distribution in the Brownian coagulation regime, and for the case of a constant input rate of single particles with beta; = 0 it is in excellent agreement with the corresponding numerical solution of Quon and Mockros. For β = 2/3 the collection kernel provides an approximate description of gravitational collection, and the corresponding power law solution conforms fairly well with observations of the tropospheric aerosol spectrum under clear air conditions for 1 ≲ r ≲ 102 μm. The chara... Abstract Analytical solutions to the steady-state kinetic coagulation equation, including sources, are presented for the case in which the collection kernel is of the form K = K0uβvβ, where K0 and β am constants (0 ≤ β < 1), and u and v represent aerosol particle volumes. Particle sources are represented by gamma distributions. The solutions look like modulated power law spectra, and rapidly approach their asymptotic power law form with increasing size. For, β = 0 the solution is equivalent to Friedlander's quasi-stationary distribution in the Brownian coagulation regime, and for the case of a constant input rate of single particles with beta; = 0 it is in excellent agreement with the corresponding numerical solution of Quon and Mockros. For β = 2/3 the collection kernel provides an approximate description of gravitational collection, and the corresponding power law solution conforms fairly well with observations of the tropospheric aerosol spectrum under clear air conditions for 1 ≲ r ≲ 102 μm. The chara...