  We prove generic versions of the no-cloning and no-broadcasting theorems,
applicable to essentially {\em any} non-classical finite-dimensional
probabilistic model that satisfies a no-signaling criterion. This includes
quantum theory as well as models supporting ``super-quantum'' correlations that
violate the Bell inequalities to a larger extent than quantum theory. The proof
of our no-broadcasting theorem is significantly more natural and more
self-contained than others we have seen: we show that a set of states is
broadcastable if, and only if, it is contained in a simplex whose vertices are
cloneable, and therefore distinguishable by a single measurement. This
necessary and sufficient condition generalizes the quantum requirement that a
broadcastable set of states commute.
