Reliable predictions of mass-loss rates are important for massive-star evolution computations. We aim to provide predictions for mass-loss rates and wind-momentum rates of O-type stars, carefully studying the behaviour of these winds as functions of stellar parameters like luminosity and metallicity. We use newly developed steady-state models of radiation-driven winds to compute the global properties of a grid of O-stars. The self-consistent models are calculated by means of an iterative solution to the equation of motion using full NLTE radiative transfer in the co-moving frame to compute the radiative acceleration. In order to study winds in different galactic environments, the grid covers main-sequence stars, giants and supergiants in the Galaxy and both Magellanic Clouds. We find a strong dependence of mass-loss on both luminosity and metallicity. Mean values across the grid are $dot{M}sim L_{ast}^{2.2}$ and $dot{M}sim Z_{ast}^{0.95}$, however we also find a somewhat stronger dependence on metallicity for lower luminosities. Similarly, the mass loss-luminosity relation is somewhat steeper for the SMC than for the Galaxy. In addition, the computed rates are systematically lower (by a factor 2 and more) than those commonly used in stellar-evolution calculations. Overall, our results agree well with observations in the Galaxy that account properly for wind-clumping, with empirical $dot{M}$ vs. $Z_ast$ scaling relations, and with observations of O-dwarfs in the SMC. Our results provide simple fit relations for mass-loss rates and wind momenta of massive O-stars stars as functions of luminosity and metallicity, valid in the range $T_{rm eff} = 28000 - 45000$,K. Due to the systematically lower $dot{M}$, our new models suggest that new rates might be needed in evolution simulations of massive stars.
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