Vertically aligned TiO2 nanotube and Al2O3 nanopore arrays have been obtained by pattern guided anodization with uniform concave depths. There are some studies about the effect of surface curvature on the growth of Al2O3 nanopores. However, the surface curvature influence on the development of TiO2 nanotubes is seldom studied. Moreover, there is no research about the effect of heterogeneous concave depths of the guiding patterns on the anodized TiO2 nanotube and Al2O3 nanopore characteristics, such as diameter, growth direction, and termination/bifurcation. In this study, focused ion beam lithography is used to create concave patterns with heterogeneous depths on flat surfaces and with uniform depths on curved surfaces. For the former, bending and bifurcation of nanotubes/nanopores are observed after the anodization. For the latter, bifurcation of a large tube into two smaller tubes occurs on concave surfaces, while termination of existing tubes occurs on convex surfaces. The growth direction of all TiO2 nanotubes is perpendicular to the local surface and thus is different on different facets of the same Ti foil. At the edge of the Ti foil where two facets meet, the nanotube growth direction is bent, resulting in a large stress release that causes the formation of cracks.