  We use the NIHAO simulations to investigate the effects of baryonic physics
on the time evolution of Dark Matter central density profiles. The sample is
made of $\approx 70$ independent high resolution hydrodynamical simulations of
galaxy formation and covers a wide mass range: 1e10< Mhalo <1e12, i.e., from
dwarfs to L* . We confirm previous results on the dependence of the inner dark
matter density slope, $\alpha$, on the ratio between stellar-to-halo mass. We
show that this relation holds approximately at all redshifts (with an intrinsic
scatter of ~0.18 in $\alpha$). This implies that in practically all haloes the
shape of their inner density profile changes quite substantially over cosmic
time, as they grow in stellar and total mass. Thus, depending on their final
stellar-to-halo mass ratio, haloes can either form and keep a substantial
density core (size~1 kpc), or form and then destroy the core and re-contract
the halo, going back to a cuspy profile, which is even steeper than CDM
predictions for massive galaxies (~1e12 Msun). We show that results from the
NIHAO suite are in good agreement with recent observational measurements of
$\alpha$ in dwarf galaxies. Overall our results suggest that the notion of a
universal density profile for dark matter haloes is no longer valid in the
presence of galaxy formation.
