The kinetic behavior of the adsorption of polymer molecules onto the surfaces of dispersed particles is examined theoretically. Under the assumptions that the surface coverage of a particle by polymer is low and the adsorption is irreversible, the distribution of the probability of the number of adsorbed polymer molecules can be approximated by a Poisson distribution (Kislenko et al., J. Colloid Interface Sci. 156, 508, 1993). A more detailed analysis reveals that, regardless of the reversibility of the adsorption process, a binomial distribution appears to be more appropriate. The deviation of the approximate Poisson distribution from the corresponding binomial distribution depends on the number of sites on a particle, S. In particular, the Poisson distribution is close to the latter only for a certain range of S; the former does not approach to the latter as S increases infinitely. (C) 1994 Academic Press, Inc.