We demonstrate a modified Hebb-Wagner approach to quantitatively estimate transference numbers for carrier conduction in thin film oxide conductors using blocking electrodes in an in-plane geometry. We report ionic transference numbers, t(i), for gadolinia-doped ceria (GDC) thin films, a model mixed ionelectron conductor, at 973K and oxygen partial pressure ranging from 0.21 atm down to approximately 10(-22) atm. Our results indicate that GDC reaches the electrolytic regime (t(i)=0.5) at an oxygen partial pressure of 5 x 10(-19) atm at 973K. This approach may be useful for understanding carrier transport mechanisms in low-dimensional oxide heterostructures with specific relevance to nanostructured energy materials.