  We examine the conditions necessary for the presence of localized magnetic
moments on adatoms with inner shell electrons in graphene. We show that the low
density of states at the Dirac point, and the anomalous broadening of the
adatom electronic level,lead to the formation of magnetic moments for
arbitrarily small local charging energy. As a result, we obtain an anomalous
scaling of the boundary separating magnetic and non-magnetic states. We show
that, unlike any other material, the formation of magnetic moments can be
controlled by an electric field effect.
