  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.
