The oxidation of rocky planet surfaces and atmospheres, which arises from the twin forces of stellar nucleosynthesis and gravitational differentiation, is a universal process of key importance to habitability and exoplanet biosignature detection. Here we take a generalized approach to this phenomenon. Using a single parameter to describe redox state, we model the evolution of terrestrial planets around nearby M-stars and the Sun. Our model includes atmospheric photochemistry, diffusion and escape, line-by-line climate calculations and interior thermodynamics and chemistry. In most cases we find abiotic atmospheric O₂ buildup around M-stars during the pre-main sequence phase to be much less than calculated previously, because the planet’s magma ocean absorbs most oxygen liberated from H₂O photolysis. However, loss of non-condensing atmospheric gases after the mantle solidifies remains a significant potential route to abiotic atmospheric O₂ subsequently. In all cases, we predict that exoplanets that receive lower stellar fluxes, such as LHS1140b and TRAPPIST- 1f and g, have the lowest probability of abiotic O₂ buildup and hence are the best targets for future biosignature searches. Key remaining uncertainties can be minimized in future by comparing our predictions for the atmospheres of hot, sterile exoplanets such as GJ1132b and TRAPPIST-1b and -c with observations.