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Using smoothed particle hydrodynamics we model giant impacts of Super-Earth mass rocky planets between an atmosphere-less projectile and an atmosphere-rich target. In this work we present results from head-on to grazing collisions. The results of the simulations fall into two broad categories: 1) one main post-collision remnant containing material from target and projectile; 2) two main post-collision remnants resulting from `erosive hit-and-run' collisions. All collisions removed at least some of the target atmosphere, in contrast to the idealised hit-and-run definition in which the target mass is unchanged. We find that the boundary between `hit-and-run' collisions and collisions that result in the projectile and target accreting/merging to be strongly correlated with the mutual escape velocity at the predicted point of closest approach. Our work shows that it is very unlikely for a single giant impact to remove all of the atmosphere. For all the atmosphere to be removed, head-on impacts require roughly the energy of catastrophic disruption (i.e. permanent ejection of half the total system mass) and result in significant erosion of the mantle. We show that higher impact angle collisions, which are more common, are less efficient at atmosphere removal than head-on collisions. Therefore, single collisions that remove all the atmosphere without substantially disrupting the planet are not expected during planet formation.