  We prove equidistribution of a generic net of small points in a projective
variety X over a function field K. For an algebraic dynamical system over K, we
generalize this equidistribution theorem to a small generic net of
subvarieties. For number fields, these results were proved by Yuan and we
transfer here his methods to function fields. If X is a closed subvariety of an
abelian variety, then we can describe the equidistribution measure explicitly
in terms of convex geometry.
