We report time-resolved optical flux and circular polarization spectroscopy of the magnetic DA white dwarf HE 1045−0908 obtained with FORS1 at the ESO VLT. Considering published results, we estimate a likely rotational period of P rot 2.7 h, but cannot exclude values as high as about 9 h. Our detailed Zeeman tomographic analysis reveals a field structure which is dominated by a quadrupole and contains additional dipole and octupole contributions, and which does not depend strongly on the assumed value of the period. A good fit to the Zeeman flux and polarization spectra is obtained if all field components are centred and inclinations of their magnetic axes with respect to each other are allowed for. The fit can be slightly improved if an oﬀset from the centre of the star is included. The prevailing surface field strength is 16 MG, but values between 10 and ∼ 75 MG do occur. We derive an eﬀective photospheric temperature of HE 1045−0908 of T eﬀ = 10 000 ± 1000 K. The tomographic code makes use of an extensive database of pre-computed Zeeman spectra (Paper I).\u
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