  The influence of the Zeeman magnetic field ($h$) on the ground state
evolution of superfluid properties from the weak coupling (BCS like) to the
strong coupling limit of tightly bound local pairs (LP) with increasing
attraction has been studied. The analysis was carried out within the
spin-polarized attractive Hubbard model, for a fixed number of particles and a
$d=3$ simple cubic lattice. The broken symmetry Hartree approximation was used.
For strong attraction and in the dilute limit, the homogeneous magnetized
superconducting phase (SC$_M$) was found in the $(h-|U|)$ and ($P-|U|$)
diagrams.
