  Using density-functional calculations, we study the effect of sp$^3$-type
defects created by different covalent functionalizations on the electronic and
magnetic properties of graphene. We find that the induced magnetic properties
are {\it universal}, in the sense that they are largely independent on the
particular adsorbates considered. When a weakly-polar single covalent bond is
established with the layer, a local spin-moment of 1.0 $\mu_B$ always appears
in graphene. This effect is similar to that of H adsorption, which saturates
one $p_z$ orbital in the carbon layer. The magnetic couplings between the
adsorbates show a strong dependence on the graphene sublattice of
chemisorption. Molecules adsorbed at the same sublattice couple
ferromagnetically, with an exchange interaction that decays very slowly with
distance, while no magnetism is found for adsorbates at opposite sublattices.
Similar magnetic properties are obtained if several $p_z$ orbitals are
saturated simultaneously by the adsorption of a large molecule. These results
might open new routes to engineer the magnetic properties of graphene
derivatives by chemical means.
