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Context. State of the art simulations of astrospheres are modelled using three-dimensional (3D) magnetohydrodynamics (MHD). An astrospheric interaction of a stellar wind (SW) with its surrounding interstellar medium (ISM) can only generate a bow shock if the speed of the interstellar inflow is higher than the fast magnetosonic speed. Aims. The differences of astrospheres at differing speeds of the ISM inflow are investigated, and the necessity of the third dimension in modelling is evaluated. Methods. The model astrosphere of the runaway O-star $λ$ Cephei is computed in both two- and three-dimensional MHD at four different ISM inflow speeds, one of which is barely faster (superfast) and one of which is slower (subfast) than the fast magnetosonic speed. Results. The two-dimensional (2D) and 3D models of astrospheres with ISM inflow speeds considerably higher than the fast magnetosonic speed are in good agreement. However, in 2D models, where no realistic SW magnetic field can be modelled, the downwind structures of the astrospheres vacillate. Models where hydrodynamic effects are not clearly dominant over the magnetic field show asymmetries, thus necessitating a 3D approach. The physical times of simulations of astrospheres with slow ISM inflows can swiftly exceed the lifetime of the corresponding star. A hitherto unobserved structure has been found downwind of the astrotail in the subfast 3D model.