Within the family, Josef Gräff claimed the following titles and honors from the extinct Herren von Graben, as whose heir he saw himself: Burggraf von Saldenhofen (Vuzenica), Herr von Kornberg, Marburg (Maribor/Marburg an der Drau), Obermarburg, Radkersburg, Neudenstein, Weinberg, Graben, Patrizier von Amsterdam.
He had inherited this claim after the death of his greatuncle Lambert (Karl) Gräff, OSBB (1848-1933). After his death, the claim passed to his son Rudolf Gräff (1919-2006).