We use the Monte Carlo method to simulate transport through a single hexagonal collimator cell and transport from the exit of the cell to the substrate. We assume a distribution function for the species entering the collimator, and that the pressure is low enough so that the transport inside the collimator cells is free molecular flow. Three-dimensional flux distributions of species exiting the collimator cell are obtained as functions of the sticking factor of the sputtered material in the collimator and the collimator aspect ratio. Specular as well as diffuse re-emission, for species which have subunity sticking factors, are considered. The larger the sticking coefficient and the higher the aspect ratio, the higher the "beaming" effect of the collimator and the smaller the fraction of species which make it through the collimator. For nonunity sticking factors, diffuse re-emission produces a more collimated beam than specular re-emission, and the fraction of the species which make it through the collimator are lower for diffuse re-emission. Collisional transport is tracked from the collimator exit to the substrate using Monte Carlo simulations for each species. The deposited film profile from a single collimator cell is computed by assuming a sticking factor of one on the substrate. The film profile over macroscopic regions of the wafer is obtained by summing the fluxes from all the collimator cells. Calculated variations in film thickness are explained in terms of collimator to wafer distance and mean free path of the sputter gas.