  The phase diagram of graphene decorated with magnetic adatoms distributed
either on a single sublattice, or evenly over the two sublattices, is computed
for adatom concentrations as low as $\sim1\%$. Within the framework of the
$s$-$d$ interaction, we take into account disorder effects due to the random
positioning of the adatoms and/or to the thermal fluctuations in the direction
of magnetic moments. Despite the presence of disorder, the magnetic phases are
shown to be stable down to the lowest concentration accessed here. This result
agrees with several experimental observations where adatom decorated graphene
has been shown to have a magnetic response. In particular, the present theory
provides a qualitative understanding for the results of Hwang et al. [Sci. Rep.
6, 21460 (2016)], where a ferromagnetic phase has been found below
$\sim30\,\text{K}$ for graphene decorated with S-atoms.
