  We use numerical simulations to investigate how the statistical properties of
dark matter (DM) haloes are affected by the baryonic processes associated with
galaxy formation. We focus on how these processes influence the spin and shape
of a large number of DM haloes covering a wide range of mass scales, from
galaxies to clusters at redshifts zero and one, extending to dwarf galaxies at
redshift two. The haloes are extracted from the OverWhelmingly Large
Simulations, a suite of state-of-the-art high-resolution cosmological
simulations run with a range of feedback prescriptions. We find that the median
spin parameter in DM-only simulations is independent of mass, redshift and
cosmology. At z=0 baryons increase the spin of the DM in the central region
(<=0.25 r_200) by up to 30 per cent when feedback is weak or absent. This
increase can be attributed to the transfer of angular momentum from baryons to
the DM, but is no longer present at z=2. We also present fits to the mass
dependence of the DM halo shape at both low and high redshift. At z=0 the
sphericity (triaxiality) is negatively (positively) correlated with halo mass
and both results are independent of cosmology. Interestingly, these
mass-dependent trends are markedly weaker at z=2. While the cooling of baryons
acts to make the overall DM halo more spherical, stronger feedback
prescriptions tend to reduce the impact of baryons by reducing the central halo
mass concentration. More generally, we demonstrate a strongly positive
(negative) correlation between halo sphericity (triaxiality) and galaxy
formation efficiency, with the latter measured using the central halo baryon
fraction. In conclusion, our results suggest that the effects of baryons on the
DM halo spin and shape are minor when the effects of cooling are mitigated, as
required by realistic models of galaxy formation, although they remain
significant for the inner halo.
