The question of the existence of asymptotic power laws, or more properly Pareto distributions, for atmospheric aerosols is examined. Present evidence that continental aerosols are asymptotically Paretian is not convincing. Improved tests for such an hypothesis are suggested. An analytical formulation of a model for the atmospheric aerosol, based on condensational growth for particles greater than a certain size, is shown to yield “characteristic” aerosol number densities whose forms are determined by the particular growth law assumed for condensation. The growth processes coupled to a reservoir of particles at the truncation point of the density, supplied by nucleation, condensation, and coagulation, cause the aerosol to “forget” its initial distribution and to approach with time the “characteristic” densities. When condensational growth proportional to particle mass is assumed, an exact Paretian density is obtained whose exponent is determined by the ratio of particle removal to growth rates. “Characteristic” densities arising from other condensational growth laws are summarized. It does not appear that these various “characteristic” densities can be resolved with present observational data for atmospheric aerosols.