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We performed predictive hybrid-DFT computations for PbTiO₃, BaTiO₃, SrTiO₃, PbZrO₃ and SrZrO₃ (001) surfaces, as well as their BaTiO₃/SrTiO₃, PbTiO₃/SrTiO₃ and PbZrO₃/SrZrO₃ (001) heterostructures. According to our hybrid-DFT computations for BO₂ and AO-terminated ABO₃ solid (001) surfaces, in most cases, the upper layer ions relax inwards, whereas the second layer ions shift upwards. Our hybrid-DFT computed surface rumpling <i>s</i> for the BO₂-terminated ABO₃ perovskite (001) surfaces almost always is positive and is in a fair agreement with the available LEED and RHEED experiments. Computed B-O atom chemical bond population values in the ABO₃ perovskite bulk are enhanced on its BO₂-terminated (001) surfaces. Computed surface energies for BO₂ and AO-terminated ABO₃ perovskite (001) surfaces are comparable; thus, both (001) surface terminations may co-exist. Our computed ABO₃ perovskite bulk Γ-Γ band gaps are in fair agreement with available experimental data. BO₂ and AO-terminated (001) surface Γ-Γ band gaps are always reduced with regard to the respective bulk band gaps. For our computed BTO/STO and PTO/STO (001) interfaces, the average augmented upper-layer atom relaxation magnitudes increased by the number of augmented BTO or PTO (001) layers and always were stronger for TiO₂-terminated than for BaO or PbO-terminated upper layers. Our B3PW concluded that BTO/STO, as well as SZO/PZO (001) interface Γ-Γ band gaps, very strongly depends on the upper augmented layer BO₂ or AO-termination but considerably less so on the number of augmented (001) layers.