Theoretical studies of the conductance of ferromagnetic and paramagnetic nanowires are performed within the framework of a three-dimensional s-d model. The attention is focused on spin-dependent conductance quantization, which manifests itself in a spectacular way when a circuit becomes open and the conduction goes down in discrete steps. A new approach is developed by assuming that in the last stages of the breaking of the nanocontact, there are fewer and fewer conduction paths, distributed at random and stretching across the contact region. Conductances are calculated within the quasiballistic regime, using the Kubo formula and a recursion Green's function technique. The results for weak ferromagnets (both majority and minority d bands intersect the Fermi surface) are qualitatively different from those for strong ferromagnets (only the minority d bands do), which may explain why experimental cumulative histograms of the conductance reveal more pronounced peaks in the case of Fe than for Ni, and consequently the latter are more sensitive to surface contaminations (oxidization).