We analyze the evolution from the weak coupling (BCS-like limit) to the strong coupling limit of tightly bound local pairs in the 2D asymmetric attractive Hubbard model, in the presence of the Zeeman magnetic eld (h). The broken symmetry Hartree approximation is used. We also apply the KosterlitzThouless scenario to determine the phase coherence temperatures. We obtain that for the spin dependent hopping integrals (t ↑ ̸ = t ↓ ) the homogeneous polarized superuid (SCM ) phase in the ground

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... for the strong attraction and lower lling can be stabilized. We nd a topological quantum phase transition (the Lifshitz type) from the unpolarized superuid phase (SC0) to SCM and tricritical point in the (h − µ) and spin polarization (P ) vs. attraction (U < 0) ground state phase diagrams. The nite temperatures phase diagrams for t ↑ ̸ = t ↓ are constructed.