A new technique, combinatorial substrate epitaxy, has been used to study the polymorphic stability and orientation relationships (ORs) for TiO 2 thin films grown by pulsed laser deposition on polycrystalline BiFeO 3 at 600°C. Electron backscatter diffraction data from 150 substrate/film pairs were analyzed to determine that anatase (A) grew with the OR (112) A ||(111) BFO and [11¯0]A||[11¯0]BFO on BiFeO 3 (BFO) substrates oriented within 35° of [100]. Rutile (R) was found on all other substrate orientations with (100) R ||(111) BFO . The in-plane orientation was primarily [001] R ||[11¯0]BFO, but some films near the anatase/rutile phase boundary were rotated by 30° so that [001] R ||[1¯21¯]BFO. Because these substrate film pairs have high-index interface planes, conventional epitaxy arguments based on two-dimensional lattice mismatch in low-index planes are considered to be limiting cases of a more general model involving the three-dimensional alignment of closest packed planes and directions, regardless of the interface plane.