The dynamics of charge separation and transport in metal-oxide nanostructures used in nanocomposite solar cells is measured by time-resolved surface photovoltage (SPV) and described by random wall, numerical simulations (RWNS). Characteristic features of anomalous diffusion and trap-limited electron transport are observed in SPV transients measured on a porous TiO2 layer sensitized with N3 dye molecules. RWNS carried out on a three-dimensional cubic lattice with an exponential distribution of states can describe these transients quantitatively over many orders of magnitude in time. The RWNS reproduce the main experimental features and permit us to extract the microscopic parameters governing electron transport such as the characteristic trap energy and the screening length.