Context :

Aims : We analyse the magnetic field geometry of the magnetic DA white dwarf PG 1015+014 with our Zeeman tomography method .

Methods : This study is based on rotation-phase resolved optical flux and circular polarization spectra of PG 1015+014 obtained with FORS1 at the ESO VLT .
Our tomographic code makes use of an extensive database of pre-computed Zeeman spectra .
The general approach has been described in Papers I and II of this series .

Results : The surface field strength distributions for all rotational phases of PG 1015+014 are characterised by a strong peak at 70 MG. A separate peak at 80 MG is seen for about one third of the rotation cycle .
Significant contributions to the Zeeman features arise from regions with field strengths between 50 and 90 MG. We obtain equally good simultaneous fits to the observations , collected in five phase bins , for two different field parametrizations : ( i ) a superposition of individually tilted and off-centred zonal multipole components ; and ( ii ) a truncated multipole expansion up to degree l = 4 including all zonal and tesseral components .
The magnetic fields generated by both parametrizations exhibit a similar global structure of the absolute surface field values , but differ considerably in the topology of the field lines .
An effective photospheric temperature of T _ { \mathrm { eff } } = 10 000 \pm 1000 K was found .

Conclusions : Remaining discrepancies between the observations and our best-fit models suggest that additional small-scale structure of the magnetic field exists which our field models are unable to cover due to the restricted number of free parameters .