  In the standard Cold Dark Matter (CDM) theory for understanding the formation
of structure in the universe, there exists a tight connection between the
properties of dark matter (DM) haloes, and their formation epochs. Such
relation can be expressed in terms of a single key parameter, namely the halo
concentration. In this work, we examine the median concentration-mass relation,
c(M), at present time, over more than 20 orders of magnitude in halo mass,
i.e., from tiny Earth-mass microhalos up to galaxy clusters. The c(M) model
proposed by Prada et al. (2012), which links the halo concentration with the
r.m.s. amplitude of matter linear fluctuations, describes remarkably well all
the available N-body simulation data down to ~10^(-6) Msun microhalos. A clear
fattening of the halo concentration-mass relation towards smaller masses is
observed, that excludes the commonly adopted power-law c(M) models, and stands
as a natural prediction for the CDM paradigm. We provide a parametrization for
the c(M) relation that works accurately for all halo masses. This feature in
the c(M) relation at low masses has decisive consequences e.g. for gamma-ray DM
searches, as it implies more modest boosts of the DM annihilation flux due to
substructure, i.e., ~35 for galaxy clusters and ~15 for galaxies like our own,
as compared to those huge values adopted in the literature that rely on such
power-law c(M) extrapolations. We provide a parametrization of the boosts that
can be safely used for dwarfs to galaxy cluster-size halos.
