Abstract : The analysis method proposed in [V. Rotival and T. Duguet, nucl-th/0702050] is applied to characterize halo properties in finite quantum systems. First, the model independence of the method is highlighted by applying it to the results of many-body calculations of light and medium-mass nuclei as well as of atom-positron complexes. Second, the dependence of halo properties on the characteristics of the nuclear energy density functional used is studied through self-consistent Hartree-Fock-Bogoliubov calculations. It is found that (a) the low-density behavior of the pairing functional and the regularization/renormalization scheme must be chosen coherently to be physically sound (b) the overall impact of pairing correlations on halo properties is very significant and is the result of two competing effects (c) however, the detailed characteristics of the pairing functional has only little importance (d) halos properties depend significantly on the ingredients of the energy density functional that influence the location of single-particle levels; i.e. effective mass, tensor terms, saturation energy. Last but not least, large scale predictions of halos among all spherical even-even nuclei are performed using specific sets of particle-hole and particle-particle energy functionals. It is shown that halos in the ground state of medium-mass nuclei might only be found at the very limit of neutron stability for a limited number of elements.