Abstract In a previous paper, the authors have presented a newly developed stochastic model of groundwater contaminant transport which is capable of accounting for the contribution of colloids flowing in the porous medium. The model is nonlinear and accounts explicitly for the exchange interactions among contaminants, colloids and the porous matrix, by means of properly introduced transition rates. The physical model is straightforward and intuitive, and it results in a system of differential equations whose dimensionality, in practical cases, is such to entail a Monte Carlo simulation to approach its solution. In this second part of the work, we explore in details the role played by those parameters which characterize the contaminant-colloid and the colloid-solid matrix interactions. A case study of Pu-239 transport inspired by a potential site for high level waste deposit at Mol (Belgium) is considered and the effects of colloid-facilitated transport is investigated under various conditions. Furthermore, an uncertainty analysis is performed to account for the uncertainties which in realistic situations affect the system and the transport phenomena. In this regard, a case study of Pu-239 transport inspired by the test site in Nevada has been considered.