In this talk we will discuss in some computational and analytical details the issue of half-metallicity in zig-zag graphene nanoribbons and nanoislands of finite width, i.e. the coexistence of metallic nature for electrons with one spin orientation and insulating nature for the electrons of opposite spin, which has been recently predicted from so-called first-principle calculations employing Density Functional Theory. We will show that, within the framework of non-relativistic quantum mechanics, like the size-extensive spin-contamination to which it relates, half-metallicity is nothing else than a methodological artefact, due to a too approximate treatment of electron correlation in the ground state.