  We study the evolution from the weak coupling (BCS-like limit) to the strong
coupling limit of tightly bound local pairs (LP's) with increasing attraction,
in the presence of the Zeeman magnetic field ($h$) for $d=2$, within the
spin-polarized attractive Hubbard model. The broken symmetry Hartree
approximation {as well as the} strong coupling expansion are used. We also
apply the Kosterlitz-Thouless (KT) scenario to determine the phase coherence
temperatures. For spin independent hopping integrals
($t^{\uparrow}=t^{\downarrow}$), we find no stable homogeneous polarized
superfluid (SC$_M$) state in the ground state for the strong attraction and
obtain that for a two-component Fermi system on a 2D lattice with population
imbalance, phase separation (PS) is favoured for a fixed particle
concentration, even on the LP (BEC) side. We also examine the influence of spin
dependent hopping integrals (mass imbalance) on the stability of the SC$_M$
phase. We find a topological quantum phase transition (Lifshitz type) from the
unpolarized superfluid phase (SC$_0$) to SC$_M$ and tricritical points in the
($h-|U|$) and ($t^{\uparrow} / t^{\downarrow} - |U|$) ground state phase
diagrams. We also construct the finite temperature phase diagrams for both
$t^{\uparrow} = t^{\downarrow}$ and $t^{\uparrow}\neq t^{\downarrow}$ and
analyze the possibility of occurrence of a spin polarized KT superfluid.
