  In this paper we consider stationary force-free magnetosphere of an aligned
rotator when plasma in the open field line region rotates differentially due to
presence of a zone with the accelerating electric field in the polar cap of
pulsar. We study the impact of differential rotation on the current density
distribution in the magnetosphere. Using split-monopole approximation we obtain
analytical expressions for physical parameters of differentially rotating
magnetosphere. We find the range of admitted current density distributions
under the requirement that the potential drop in the polar cap is less than the
vacuum potential drop. We show that the current density distribution could
deviate significantly from the ``classical'' Michel distribution and could be
made almost constant over the polar cap even when the potential drop in the
accelerating zone is of the order of 10 per cents of the vacuum potential drop.
We argue that differential rotation of the open magnetic field lines could play
an important role in adjusting between the magnetosphere and the polar cap
cascade zone and could affect the value of pulsar breaking index.
