We present a parameter study of WR-type mass loss, based on the PoWR hydrodynamic model atmospheres. These new models imply that optically thick WR-type winds are generally formed close to the Eddington limit. This is demonstrated for the case of hydrogen rich WNL stars, which turn out to be extremely massive, luminous stars with progenitor masses above ≈ 80 M⊙. We investigate the dependence of WR-type mass loss on various stellar parameters, including the metallicity Z. The results depend strongly on the L/M ratio, the stellar temperature T*, and the assumed wind clumping. For high L/M ratios, strong WR-type winds can be maintained down to very low Z. Even for primordial massive stars we predict considerable mass loss if their surfaces are self-enriched by primary elements.