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We use the NIHAO (Numerical Investigation of Hundred Astrophysical Objects) cosmological simulations to investigate the effects of baryonic physics on the time evolution of dark matter central density profiles. The sample is made of ≈70 independent high-resolution hydrodynamical simulations of galaxy formation and covers a wide mass range: 1010 ≲ Mhalo/M⊙ ≲ 1012, i.e. from dwarfs to L*. We confirm previous results on the dependence of the inner dark matter density slope, α, on the ratio between stellar-to-halo mass, Mstar/Mhalo. We show that this relation holds approximately at all redshifts (with an intrinsic scatter of ~0.18 in α measured between 1 and 2 per cent of the virial radius). 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 Mstar/Mhalo ratio, haloes can either form and keep a substantial density core (Rcore ~ 1 kpc), or form and then destroy the core and recontract the halo, going back to a cuspy profile, which is even steeper than cold-dark-matter predictions for massive galaxies (1012 M⊙). We show that results from the NIHAO suite are in good agreement with recent observational measurements of α 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 Overall our results suggest that the notion of a universal density profile for dark matter haloes is no longer valid in the presence of galaxy formation. [ABSTRACT FROM AUTHOR]