The adhesion of hard spheres, modeling particles of biological interest (proteins, bacteria, cells), on flat surfaces is investigated by means of Monte Carlo simulations. These computations include the Brownian diffusion of the particles in the bulk fluid, as well as the systematic displacement due to the gravitational field. The size of the particles influences directly both diffusion coefficient and net weight, with the consequence that the coverage at the jamming limit depends on this parameter. Results obtained in a former paper based on a lattice model are confirmed by the present continuous space model. In order to gain a better understanding of the adsorption competition of two types of particles, the proposed model is applied to the case of binary mixtures of spheres. For polydispersed suspensions, various parameters determine the final coverage, as well as the distribution of the small and large particles on the surface: the radii of the particles and the respective proportions of them in the infinitely large reservoir from which they are randomly selected. In this way, it is shown that the chronology of the adhesion of the small and large particles strongly influences the final number of each type of spheres fixed on the surface. Qualitatively, the present results resemble those obtained with disks placed by means of a classical random sequential adsorption mechanisms. Quantitatively, however, the number densities and coverage values determined in this way are significantly different due to the inclusion of the gravity and of the diffusion in the model.