  Given a closed positive current T on a compact Kahler manifold X, we
introduce the notion of non-pluripolar product relative to T of closed positive
(1,1)-currents. We recover the well-known non-pluripolar product when T is the
current of integration along X. Our main results are a monotonicity property of
relative non-pluripolar products, a necessary condition for currents to be of
relative full mass intersection in terms of Lelong numbers, and the convexity
of weighted classes of currents of relative full mass intersection. The former
two results are new even when T is the current of integration along X.
