A high fibered power of a family of varieties of general type dominates   a variety of general type
  We prove the following theorem:   Fibered Power Theorem: Let $X\rar B$ be a smooth family of positive dimensional varieties of general type, with $B$ irreducible. Then there exists an integer $n>0$, a positive dimensional variety of general type $W_n$, and a dominant rational map $X^n_B \das W_n$. 
Dan Abramovich