Giant neutron halos are studied in the framework of the Skyrme-Hartree-Fock-Bogoliubov approach. The appearance of such structures depends sensitively on the effective interaction adopted. This is illustrated by comparing the predictions of SLy4 and SkI4 in the Zr isotopic chain. The latter force predicts a neutron halo in the Zr chain with A > 122 due to weakly bound p orbitals. The structure of the halo is analyzed and the anti-halo effect due to pairing is discussed.