We report on the high mobility wide electron slabs with enhanced correlation effects by tailoring the polarization effects in a functionally graded ZnMgO/ZnO heterostructures. The characteristics of three-dimensional (3D) spreading electrons are evidenced by the capacitance-voltage profiling and the quantization of 3D Fermi surface in magneto-transport measurements. Despite the weak spin-orbit interaction, such electron slabs are spin-polarized with a large zero-field spin splitting energy, which is induced by the carrier-mediated ferromagnetism. Our results suggest that the vast majority of electrons are localized at the surface magnetic moment which does not allow spin manipulations, and only in the region visited by the itinerant carriers that the ferromagnetic exchange interactions via coupling to the surface local moments contribute to the spin transport. The host ferromagnetism is likely due to the formation of Zn cation vacancies on the surface regime induced by the stabilization mechanism and strain-relaxation in ZnMgO polar ionic surface.