  Recent numerical studies of the dark matter density profiles of massive
galaxy clusters ($M_{\rm halo} > 10^{15}$M$_{\odot}$) show that their median
radial mass density profile remains unchanged up to $z > 1$, displaying a
highly self-similar evolution. We verify this by using the data set of the THE
THREE HUNDRED project, i.e. 324 cluster-sized haloes as found in full physics
hydrodynamical simulations. We track the progenitors of the mass-complete
sample of clusters at $z=0$, and find that their median shape is already in
place by $z=2.5$. However, selecting a dynamically relaxed subsample ($\sim16$
per cent of the clusters), we observe a shift of the scale radius $r_s$ towards
larger values at earlier times. Classifying the whole sample by formation time,
this evolution is understood as a result of a two-phase halo mass accretion
process. Early-forming clusters -- identified as relaxed today -- have already
entered their slow accretion phase, hence their mass growth occurs mostly at
the outskirts. Late-forming clusters -- which are still unrelaxed today -- are
in their fast accretion phase, thus the central region of the clusters is still
growing. We conclude that the density profile of galaxy clusters shows a
profound self-similarity out to redshifts $z\sim2.5$. This result holds for
both gas and total density profiles when including baryonic physics, as
reported here for two rather distinct sub-grid models.
