Holomorphic maps onto Kaehler manifolds with non-negative Kodaira   dimension
  The paper studies the deformation theory of a holomorphic surjective map from a normal compact complex space to a compact Kaehler manifold and describes the component of the space of holomorphic maps, generalizing results in the projective case by Kebekus and the authors. 
Jun-Muk Hwang and Thomas Peternell