  Several pairing schemes currently used to describe superfluid nuclei through
Hartree-Fock-Bogolyubov (HFB) calculations are briefly reviewed. We put a
particular emphasis on the regularization recipes used in connection with
zero-range forces and on the density dependence which usually complement their
definition. Regarding the chosen regularization process, the goal is not only
to identify the impact it may or may not have on pairing properties of nuclei
through spherical 1D HFB calculations but also to assess its tractability for
systematic axial 2D and 3D mean-field and beyond-mean-field calculations.
