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Here we briefly report on results of self-consistent numerical modeling of adifferentially rotating force-free magnetosphere of an aligned rotator. We showthat differential rotation of the open field line zone is significant foradjusting of the global structure of the magnetosphere to the current densityflowing through the polar cap cascades. We argue that for most pulsarsstationary cascades in the polar cap can not support stationary force-freeconfigurations of the magnetosphere.Comment: 5 pages, 4 figures. Presented at the conference "Isolated Neutron  Stars: from the Interior to the Surface", London, April 24-28, 2006; to  appear in Astrophysics and Space Science. Significantly revised version, a  mistake found by ourselfs in the numerical code was corrected, all presented  results are obtained with the correct version of the cod

Force-free magnetosphere of an aligned rotator with differential rotation of open magnetic field lines