We study the C*-convex set of unital entanglement breaking (EB-) maps on matrix algebras. General properties and an abstract characterization of C*-extreme points are discussed. It is shown that a unital EB-map from d1 x d1 matrix algebra to d2 x d2 matrix algebra is C*-extreme if and only if it has Choi-rank equal to d2. This is based on a joint work with R. Devendra, N. Mallick and K. Sumesh.