Experiments with the self-assembly of nanoparticles at liquid interfaces suggest that cooperative and slow dynamical processes due to particle crowding at the interface govern the adsorption and properties of the final assembly. Here we report a numerical approach to studying nonequilibrium adsorption, which elucidates these experimental observations. The analysis of particle rearrangements shows that local ordering processes are directly related to adsorption events at high interface coverage. Interestingly, this feature and the mechanism coupling local ordering to adsorption do not seem to change qualitatively upon increasing particle size polydispersity, although the latter changes the interface microstructure and its final properties. Our results indicate how adsorption kinetics can be used for the fabrication of 2D nanocomposites with controlled microstructure.