Non force-free cylindrical equilibrium of the magnetically driven relativistic MHD flows is investigated as a model of astrophysical jets/winds. This work is a generalization of the previous work Nitta (1995). We consider the situation that the magnetic field lines emanated from the central object are rotating, and the frozen plasmas are magnetically accelerated outward and construct a self-organized magnetosphere due to the Lorentz force and the inertial force. Recent observations revealed that many objects have a hybrid structure of collimated jet and non-collimated wind regardless with species of the central object, e.g. YSO’s, stars, pulsars or AGN’s. In order to explain these structures, we present a model that the magnetosphere has a hybrid asymptotic structure: the cylindrical jet and the conical wind fill the infinitely distant polar region and the lower latitude region, respectively. The asymptotically conical wind was investigated in the previous paper (Nitta 1994). Here we investigate the asymptotically cylindrical jet at ‘finite cylindrical radius’ from the rotational axis. In this case, the inertial force is important for the force balance because a fraction of the flows having finite angular momentum converges to finite cylindrical radius.