  We analyze the evolution from the weak coupling (BCS-like limit) to the
strong coupling limit of tightly bound local pairs (LP's) in the 2D asymmetric
attractive Hubbard model, in the presence of the Zeeman magnetic field ($h$).
The broken symmetry Hartree approximation is used. We also apply the
Kosterlitz-Thouless (KT) scenario to determine the phase coherence
temperatures. We obtain that for the spin dependent hopping integrals
($t^{\uparrow}\neq t^{\downarrow}$) the homogeneous polarized superfluid
(SC$_M$) phase in the ground state for the strong attraction and lower filling
can be stabilized. We find a topological quantum phase transition (Lifshitz
type) from the unpolarized superfluid phase (SC$_0$) to SC$_M$ and tricritical
point in the ($h-\mu$) and spin polarization ($P$) vs. attraction ($U<0$)
ground state phase diagrams. The finite temperatures phase diagrams for
$t^{\uparrow}\neq t^{\downarrow}$ are constructed.
