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An atmosphere may be described as globally super-rotating if its total zonal angular momentum exceeds that associated with solid-body co-rotation with the underlying planet. In this paper, we discuss the dependence of global super-rotation in terrestrial atmospheres on planetary rotation rate. This dependence is revealed through analysis of global super-rotation in idealised General Circulation Model experiments with time-independent axisymmetric forcing, compared with estimates for global super-rotation in Solar System atmospheres. Axisymmetric and three-dimensional experiments are conducted. We find that the degree of global super-rotation in the three-dimensional experiments is closely related to that of the axisymmetric experiments, with some differences in detail. A scaling theory for global super-rotation in an axisymmetric atmosphere is derived from the Held-Hou model. At high rotation rate, our numerical experiments inhabit a regime where global super-rotation scales geostrophically, and we suggest that the Earth and Mars occupy this regime. At low rotation rate, our experiments occupy a regime determined by angular momentum conservation, where global super-rotation is independent of rotation rate. Global super-rotation in our experiments saturates at a value significantly lower than that achieved in the atmospheres of Venus and Titan, which instead occupy a regime where global super-rotation scales cyclostrophically. This regime can only be accessed when eddy induced up-gradient angular momentum transport is sufficiently large, which is not the case in our idealised numerical experiments. We suggest that the 'default' regime for a slowly rotating planet is the angular momentum conserving regime, characterised by mild global (and local) superrotation.