This paper investigates the power loads at the inner and outer divertor targets of attached, Ohmic L-mode, deuterium plasmas in the TCV tokamak, in various experimental situations using an Infrared thermography system. The study comprises variations of the outer divertor leg length and target flux expansion, the plasma current and a reversal of the magnetic field direction. The direct impact of the divertor magnetic geometry on scrape-off layer (SOL) transport-parameterised by the SOL power fall-off length lambda(q,u,) the divertor spreading factor S-u and the in-out power asymmetry-is reported for constant core properties. The in-out power asymmetry increases, either with the divertor leg length, or the target flux expansion. The SOL width lambda(q,u) scales positively with divertor leg length, with a strength that depends on the field direction and differs between the inner and outer divertor. This implies a parametric dependence of lambda(q,u) that is not explicitly included in current multi-machine scaling laws. The divertor spreading factor at the target S = S(u)f(x), where f(x) is the target flux expansion, appears unaffected by changes in the divertor geometry and in the plasma current, is independent of the magnetic field direction and is similar between inner and outer divertor. Possible interpretations of these observations using an ad-hoc analytical purely conductive model for the SOL, by ion drifts or by asymmetric turbulent cross-field transport in the divertor are presented. The observed values of lambda(q,u) are related to existing L-mode and H-mode scaling laws and to similar studies in other tokamaks. Finally, potential implications of these findings for future larger fusion machines are discussed.