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Mobile charge carriers in heterostructured nanoparticles are relevant for applications requiring charge separation and extraction. We investigate the benchmark systems CdSe-CdS core-shell quantum dots and quantum dots in quantum rods by optical and THz pump-probe spectroscopy. We relate photoconductivity and carrier location and observe that only shell-located electrons in quantum rods contribute to an observable photoconductivity. Despite the shallow electron confinement in the quasi-type II heterostructures, core-located carriers are bound into immobile excitons that respond on external electrical fields by polarization.