  Intermediate-mass, magnetic chemically peculiar (Ap) stars provide a unique
opportunity to study the topology of stellar magnetic fields in detail and to
investigate magnetically driven processes of spot formation. Here we aim to
derive the surface magnetic field geometry and chemical abundance distributions
for the extraordinary Ap star HD 75049. This object hosts a surface field of
~30 kG, one of the strongest known for any non-degenerate star. We used
time-series of high-resolution HARPS intensity and circular polarisation
observations. These data were interpreted with the help of magnetic Doppler
imaging and model atmospheres incorporating effects of a non-solar chemical
composition and a strong magnetic field. We refined the rotational period of HD
75049 to Prot=4.048267+/-0.000036 d. We also derived basic stellar parameters,
Teff=10250+/-250 K and logg=4.3+/-0.1. Magnetic Doppler imaging revealed that
the field topology of HD 75049 is poloidal and dominated by a dipolar
contribution with a peak surface field strength of 39 kG. At the same time,
deviations from the classical axisymmetric oblique dipolar configuration are
significant. Chemical surface maps of Si, Cr, Fe, and Nd show abundance
contrasts of 0.5-1.4 dex, which is low compared with many other Ap stars. Nd is
found to be enhanced close to the magnetic pole, whereas Si and Cr are
concentrated predominantly at the magnetic equator. The iron distribution shows
low-contrast features both at the magnetic equator and the pole. The morphology
of the magnetic field and the properties of chemical spots in HD 75049 are
qualitatively similar to those of Ap stars with weaker fields. Consequently,
whatever mechanism forms and sustains global magnetic fields in
intermediate-mass main-sequence stars, it operates in the same way over the
entire observed range of magnetic field strengths.
