Properties of ionic distributions of mixtures of atomic (Na+, Mg2+, Cl-) and molecular (spennidine(3+)) ions in the vicinity of DNA have been studied by the Monte Carlo simulation method, within the frame of a continuum dielectric approach. Several models differing by the level of approximations have been considered and compared. In one of these models the DNA phosphate charge distribution is described by point charges in a double helical array corresponding to B-DNA, thus in an idealized way incorporating the major and minor groove structure. Ion distribution profiles, ion binding properties, and competition effects in the association of the different counterions to DNA have been studied. Particular attention has been paid to the importance of the discrete distribution of the three charges on the spermidine molecular model. The work has shown that the behavior of complex multivalent ions differs strongly from the properties of simple metal ions of the same valence. The competitive behavior and binding properties of the spermidine molecule modeled with distributed charges appear to be reduced from those expected for point charge (or spherical) three-valent ions, even compared to the predictions of the Poisson-Boltzmann approximation, and more likely correspond to the behavior of atomic divalent ions. The results of binding properties was found to be in qualitative agreement with existing NMR diffusion studies of polyamine association to DNA.