  We present a theory of graphene quantum rings designed to produce degenerate
shells of single particle states close to the Fermi level. We show that
populating these shells with carriers using a gate leads to correlated ground
states with finite total electronic spin. Using a combination of tight-binding
and configuration interaction methods we predict ground state and total spin of
the system as a function of the filling of the shell. We show that for smaller
quantum rings, the spin polarization of the ground state at half filling
depends strongly on the size of the system, but reaches a maximum value after
reaching a critical size.
