We observe the effect of non-zero magnetization m on the superconducting ground state of the one-dimensional Hubbard model with off-diagonal Coulomb repulsion X. For t/2\lesssim X\lesssim 2t/3, the system first manifests Fulde–Ferrell–Larkin–Ovchinnikov oscillations in the pair–pair correlations. For m= m 1 a kinetic energy driven macroscopic phase separation into low density superconducting domains and high density polarized walls takes place. For m> m 2 the domains fully localize, and the system eventually becomes a ferrimagnetic insulator.