In this paper, diffusional transport of multi-component mixtures within the framework of a three-dimensional lattice gas is studied using dynamic Monte Carlo simulations. The mobile species, instantaneously hopping from one site to another, are assumed to have no mutual interactions, other than the usual ‘hard core’ interactions. Most strikingly, percolation phenomena occur for multi-component mixtures with significant differences in mobility. These greatly reduce the flux of the mobile component and cause failure of the standard macroscopic theories, including, e.g., the Maxwell–Stefan theory. Furthermore, we demonstrate that the well-known correlation effect disappears for systems in which gradients in the vacancy concentration are present. For systems in which co-operative displacements of two or more molecules are allowed to occur the effect of correlation between successive jumps vanishes, while the plot of the mobility versus occupancy shows a maximum. This intricate relation between mobility and occupancy again complicates the use of standard theories for describing mass transport.