The band alignments at nonpolar surfaces and heterointerfaces of , , and polymorphs, and three related group-III oxides, namely, , , and , are investigated by using first-principles calculations. A non-self-consistent dielectric-dependent hybrid functional approach is adopted on top of semilocal density-functional calculations by using the Perdew-Burke-Ernzerhof functional tuned for solids (PBEsol) to accelerate the band alignment evaluation that involves surface and interface calculations. Among the five crystal structures considered, namely, corundum, β-gallia, κ-alumina, bixbyite (C-type rare earth), and A-type rare earth, the lowest energy phases are corundum, β-gallia, A-type rare earth, and bixbyite for , , , and the others, respectively, within PBEsol calculations. The ionization potential typically decreases in the order , , , , , and within the same crystal structure and surface termination. This tendency is enhanced by the atomic relaxation-induced surface dipoles, where smaller cations tend to relax toward the bulk side compared to O ions, while larger cations tend to relax toward the vacuum side. The ionization potential and electron affinity differences at unrelaxed surfaces are good indicators of the interfacial valence- and conduction-band offsets, respectively, for / with a relatively small mismatch in the lattice parameters of the two phases.