  We make a conjecture about mean curvature flow of Lagrangian submanifolds of
Calabi-Yau manifolds, expanding on \cite{Th}. We give new results about the
stability condition, and propose a Jordan-H\"older-type decomposition of
(special) Lagrangians. The main results are the uniqueness of special
Lagrangians in hamiltonian deformation classes of Lagrangians, under mild
conditions, and a proof of the conjecture in some cases with symmetry: mean
curvature flow converging to Shapere-Vafa's examples of SLags.
