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Relativistic jets are formed by plasma injected into the rapidly rotating magnetosphere of accretion disks. The accretion disk generates a dipolar or a quadrupolar magnetosphere which also immerses the black hole. We present self-consistent solutions for the structure of this magnetosphere based on the Grad-Schlüter-Shafranov equation for the poloidal magnetic flux. The resulting supermagnetosonic jets consist of a nested family of magnetic surfaces filled with normal plasma flowing along thedoi:10.1017/s0074180900190679 fatcat:za5innx2jndplogfjq5qxcnbqq