  We present cosmological hydrodynamical simulations of eight Milky Way-sized
haloes that have been previously studied with dark matter only in the Aquarius
project. For the first time, we employ the moving-mesh code AREPO in zoom
simulations combined with a comprehensive model for galaxy formation physics
designed for large0 cosmological simulations. Our simulations form in most of
the eight haloes strongly disc-dominated systems with realistic rotation
curves, close to exponential surface density profiles, a stellar-mass to
halo-mass ratio that matches expectations from abundance matching techniques,
and galaxy sizes and ages consistent with expectations from large galaxy
surveys in the local Universe. There is no evidence for any dark matter core
formation in our simulations, even so they include repeated baryonic outflows
by supernova-driven winds and black hole quasar feedback. For one of our
haloes, the object studied in the recent `Aquila' code comparison project, we
carried out a resolution study with our techniques, covering a dynamic range of
64 in mass resolution. Without any change in our feedback parameters, the final
galaxy properties are reassuringly similar, in contrast to other modelling
techniques used in the field that are inherently resolution dependent. This
success in producing realistic disc galaxies is reached, in the context of our
interstellar medium treatment, without resorting to a high density threshold
for star formation, a low star formation efficiency, or early stellar feedback,
factors deemed crucial for disc formation by other recent numerical studies.
