When an electron is confined to a triangular atomic thick layer of graphene [1-5] with zig-zag edges, its energy spectrum collapses to a shell of degenerate states at the Fermi level (Dirac point) [6-9]. The degeneracy is proportional to the edge size and can be made macroscopic. This opens up the possibility to design a strongly correlated electronic system as a function of fractional filling of the zero-energy shell, in analogy to the fractional quantum Hall effect in a quasi-two-dimensional electron gas, but without the need for a high magnetic field. In this work we show that electronic correlations, beyond the Hubbard model[6,7] and mean-field density functional theory (DFT) [7,8] play a crucial role in determining the nature of the ground state and the excitation spectrum of triangular graphene quantum dots as a function of dot size and filling fraction of the shell of zero-energy states. The interactions are treated by a combination of DFT, tight-binding, Hartree-Fock and configuration interaction methods (TB-HF-CI) and include all scattering and exchange terms within second nearest neighbors as well as interaction with metallic gate. We show that a half filled charge neutral shell leads to full spin polarization of the island but this magnetic moment is completely destroyed by the addition of a single electron, in analogy to the effect of skyrmions on the quantum Hall ferromagnet [11-14] and spin depolarization in electrostatically defined semiconductor quantum dots[15-18]. The depolarization of the ground state is predicted to result in blocking of current through a graphene quantum dot due to spin blockade (SB) .