A note on unital full amalgamated free products of quasi-diagonal   C*-algebras
  In the paper, we consider the question whether a unital full amalgamated free product of quasidiagonal C*-algebras is quasidiagonal again. We give a sufficient condition such that a unital full amalgamated free product of quasidiagonal C*-algebras with amalgamation over a finite dimensional C*- algebra is quasidiagonal. Applying this result, we conclude that a unital full free product of two AF algebras with amalgamation over a finite-dimensional C*-algebra is AF if there are faithful tracial states on each of these two AF algebras such that the restrictions on the common subalgebra agree. 
Qihui Li, Don Hadwin, Jiankui Li, Xiujuan Ma and Junhao Shen
math.OA