  We consider magnetospheric structure of rotating neutron stars with
internally twisted axisymmetric magnetic fields. The twist-induced and
rotation-induced toroidal magnetic fields align/counter-align in different
hemispheres. Using analytical and numerical calculations (with PHAEDRA code) we
show that as a result the North-South symmetry is broken: the magnetosphere and
the wind become "angled", of conical shape. Angling of the magnetosphere
affects the spindown (making it smaller for mild twists), makes the return
current split unequally at the Y-point, produces anisotropic wind and linear
acceleration that may dominate over gravitational acceleration in the Galactic
potential and give a total kick up to $\sim 100$ km/s. We also consider
analytically the structure of the Y-point in the twisted magnetosphere, and
provide estimate of the internal twist beyond which no stable solutions exist:
over-twisted magnetospheres must produce plasma ejection events.
