In the 1990s, Ullmo and Zhang independently proved the Bogomolov Conjecture, about the geometry of points of small canonical height on abelian varieties; a key ingredient was an equidistribution statement for these points (that they proved jointly with Szpiro). In joint work with Myrto Mavraki, we study a related problem in the setting where A is a family of abelian varieties, splitting as a product of elliptic curves. We prove an equidistribution result that applies to Unlikely Intersection questions and relates to some work of Masser and Zannier.