What is the Osage Mineral Estate? The Osage Mineral Estate is the oil, gas, and other Minerals sub-surface of the approximately 1.47 million acre Osage Reservation. Who owns the Osage Mineral Estate? Section 3 of the 1906 Act establishes that the Osage Nation is the beneficial owner the Osage Mineral Estate.The United States holds title to the Osage Mineral Estate in trust for the Osage Nation. No