The band alignments at nonpolar surfaces and heterointerfaces of Al 2 O 3 , Ga 2 O 3 , and In 2 O 3 polymorphs, and three related group-III oxides, namely, Sc 2 O 3 , Y 2 O 3 , and La 2 O 3 , 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 Al 2 O 3 , Ga 2 O 3 , La 2 O 3 , and the others, respectively, within PBEsol calculations. The ionization potential typically decreases in the order Al 2 O 3 , Ga 2 O 3 , In 2 O 3 , Sc 2 O 3 , Y 2 O 3 , and La 2 O 3 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 Al 2 O 3 /Ga 2 O 3 with a relatively small mismatch in the lattice parameters of the two phases.