Renormalization analysis discussed in Giona et al. (1996a, Chem. Engng Sci., 51, 4717-4729) is applied to study diffusion and convection on fractals. Sorption properties and moment analysis are developed on fractals. Extension theory is applied to diffusion in the presence of multiple- length hopping. The case of diffusion in random and heterogeneous structures is also addressed. Finally, renormalization of diffusion with convective bias on fractals is developed.