  The Torsion Anomalous Conjecture (TAC) states that a subvariety V of an
abelian variety A has only finitely many maximal torsion anomalous
subvarieties. In this work we prove, with an effective method, some cases of
the TAC when the ambient variety A has CM, generalising our previous results in
products of CM elliptic curves. When V is a curve, we give new results and we
deduce some implications on the effective Mordell-Lang Conjecture.
