This work reports a systematic study of the evolution of charge transport mechanism in granular ultra-thin films of palladium of thickness varying between 6nm and 2nm. While the films with thickness > 4nm exhibit metallic behaviour, that at 3nm thickness undergoes a metal-insulator transition at 19.5K. In contrast, the 2nm thick film remained insulating at all temperatures. with transport following Mott's variable range hopping. At room temperature, while the thicker film exhibit resistance decrease on H$_2$ exposure. the insulating film showed an anomalous initial resistance increase before switching to a subsequent decrease. The nanostructure dependent transport and the ensuing H$_2$ response is modeled on a percolation model, which also explores the relevance of film thickness as a macroscopic control parameter to engineer the desired system response in granular metal films.
