Abstract. We consider the magnetic interconnection of Saturn's northern and southern polar regions controlled by the interplanetary magnetic field (IMF), studying in particular the more complex and interesting case of southward IMF, when the Kronian magnetospheric magnetic field structure is the most twisted. The simpler case of northward IMF is also discussed. Knowledge of the magnetospheric magnetic field structure is very significant, for example, for investigation of the electric fields and field-aligned currents in Saturn's environment, particularly those which cause the auroral emissions. Here we modify the paraboloid magnetospheric magnetic field model employed in previous related studies by including higher multipole terms in Saturn's internal magnetic field, required for more detailed considerations of inter-hemispheric conjugacy, together with inclusion of a spheroidal boundary at the ionospheric level. The model is employed to map Southern Hemisphere auroral regions observed by the Hubble Space Telescope (HST) in 2008 under known IMF conditions to both the equatorial plane and the northern ionosphere. It is shown that the brightest auroral features map typically to the equatorial region between the central ring current and the outer magnetosphere, and that auroral features should be largely symmetric between the two hemispheres, except for a small poleward displacement and latitudinal narrowing in the Northern Hemisphere compared with the Southern Hemisphere due to the quadrupole field asymmetry. The latter features are in agreement with the conjugate auroras observed under near-equinoctial conditions in early 2009, when IMF data are not available.