The extreme shaping capabilities of the TCV tokamak have been used to investigate the effect of plasma geometry on the confinement of non-recycling trace impurities injected by means of the laser blow-off technique. The progression of the injected silicon in the core of TCV Ohmic limiter plasmas was followed by the 200-channel soft x-ray (SXR) photodiode array with good spatial and temporal resolution. The results show that the plasma triangularity and elongation play an important role in the impurity confinement time, tau(imp). Remarkably, the increase of elongation from kappa = 1.6 to 2.3 produces a threefold reduction of tau(imp) while the electron energy confinement time, tau(Ee), remains almost constant. tau(imp) is fairly constant in the triangularity scan for delta > 0.2, while there is a marked increase for lower values, leading to tau(imp) > 100 ms for negative triangularities. The increase of the toroidal magnetic field, B-T, from B-T = 0.92 to 1.47 T produces a decrease in the confinement time by almost a factor of 2. Simulation of the evolution of the line-integrated SXR signals, performed by the one-dimensional code STRAHL, provided both central and peripheral values of the transport coefficients together with estimates of the radial profiles. The simulations show that anomalous transport is dominant over neoclassical transport, except near the plasma centre. Interestingly, the convective velocity is positive (outwardly directed) in all limiter cases.