  We study dualities in off-shell 4D N = 2 supersymmetric sigma-models, using
the projective superspace approach. These include (i) duality between the real
O(2n) and polar multiplets; and (ii) polar-polar duality. We demonstrate that
the dual of any superconformal sigma-model is superconformal. Since N = 2
superconformal sigma-models (for which target spaces are hyperkahler cones)
formulated in terms of polar multiplets are naturally associated with Kahler
cones (which are target spaces for N = 1 superconformal sigma-models),
polar-polar duality generates a transformation between different Kahler cones.
In the non-superconformal case, we study implications of polar-polar duality
for the sigma-model formulation in terms of N = 1 chiral superfields. In
particular, we find the relation between the original hyperkahler potential and
its dual. As an application of polar-polar duality, we study self-dual models.
