Two models of particle depositions with different adhesion dynamics have been developed and studied using Monte Carlo simulations. They have been compared for the complete range of Peclet numbers and they differ in the particle-adhesion dynamics, with an adherence-potential barrier in one of them. In general, the time course of the two models is different in ballistic cases, but similar in diffusive cases. Thus, they complement each other, enabling a description of the morphology for most cases. Depending on their deposits, these systems have been characterized morphologically, as compact, homogeneous, or open. They have also been described by the following parameters, which have been analyzed: from the first to the fourth moments, porosity, and the fractal dimension. Also, the time course of the parameters has been studied and described, especially the Anomalous and Family-Vicsek scaling. The third and fourth moments and the fractal dimension have been characterized, defining different stages in their time course, and studying their behavior for the complete range of Peclet numbers. Moreover, the inclusion of an adherence-potential barrier enables the description of new universality class intervals needed to explain recent experimental systems, e.g., at the edges of evaporated drops of colloidal suspensions, electro-convection on nematic liquid crystals, and polynuclear growth model. Finally, the characterization of the systems required not only a dynamic exponent (β) by universality classes but also a third (skewness) and fourth (kurtosis) moments for a complete description.
