  We prove the several variable version of the classical equidistribution
theorem for Fekete points of a compact subset of the complex plane, which
settles a well-known conjecture in pluri-potential theory. The result is
obtained as a special case of a general equidistribution theorem for Fekete
points in the setting of a given holomorphic line bundle over a compact complex
manifold. The proof builds on our recent work "Capacities and weighted volumes
for line bundles".
