  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 Prot ~
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 ~75MG do occur. We derive an effective photospheric
temperature of HE 1045-0908 of Teff = 10000 +/- 1000 K. The tomographic code
makes use of an extensive database of pre-computed Zeeman spectra (Paper I).
