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We have grown epitaxial incommensurate alfa-Fe2O3 thin films on alfa-Al2O3(0001), SrTiO3(111), and LaAlO3(001) substrates, identifying hematite as single iron oxide phase stabilized. We demonstrate that a different lattice coupling behavior as a function of the selected oxide substrate mediates the epitaxial character. Single-oriented alfa-Fe2O3(0001) layers are obtained on alfa-Al2O3(0001) and SrTiO3(111) substrates, whereas on the LaAlO3(001) substrate, the hematite layer is found to grow along the r-plane to adapt its hexagonal lattice on the cubic lattice of the substrate, evidencing a single-oriented (11̅02) layer. In the film plane, crystallographic axes of alfa-Fe2O3(0001) are collinear with the alfa-Al2O3(0001) ones, while a rotation of 30° is found between those of alfa-Fe2O3(0001) and SrTiO3(111). On LaAlO3(001), alfa-Fe2O3(11̅02) adopts an in-plane orthorhombic structure rotated 45° respect to the substrate lattice. The crystallographic domain size and the crystalline order are dependent on the incommensurate lattice coupling mechanism. Larger values are obtained for layers grown on alfa-Al2O3(0001), while lower values correspond to the hematite deposited on LaAlO3(001). Moreover, an Fe-O elongation and Fe-Fe contraction of first neighbors distances as well as a dependency on surface flatness as a function of the substrate lattice parameter is also found.