The electron temperature, pressure and density pro les from an extreme variety of shaped Ohmically heated sawtoothing plasmas in TCV ( Tokamak a Configuration Variable, B-T < 1.5T, R-0 = 0.88 m, a < 0.25 m) are compared to model predictions drawing from two bodies of theory. One of these is based on the assumption of stationary magnetic entropy and predicts sti toroidal current, and consequently Ohmically relaxed electron temperature pro les. The second theory is based on the assumption of approximate conservation of the rst and second adiabatic invariants during particle transport and predicts density pro les closely related to the safety factor. The robustness of these predictions in Ohmically heated plasmas is confirmed by systematic observations in TCV.