In the magnetosphere of a planet which has its rotation axis aligned with the solar wind flow direction and its magnetic dipole axis significantly tilted to its rotation axis, solar-wind-driven magnetospheric convection can transport plasma throughout the magnetosphere; although corotation is present, it does not produce a closed flow region (normally identified with the plasmasphere) and thus does not impede penetration of convection into the inner magnetosphere. The difference from the conventional theory of plasmasphere formation lies in the fact that, with the assumed geometry, the spatial pattern of magnetospheric convection is steady in the corotating rather than in the fixed frame of reference. Uranus at the present epoch closely approximates to this geometry, and hence magnetospheric convection is expected to be the dominant transport process in the Uranium magnetosphere, leading to transport times comparable to the estimated flow times of 30--40 hours.