Large indecomposable roots of Ext

Let D be any p-cotorsion free (abelian) group. We construct a proper class of indecomposable torsion free groups G such that Ext(D,G)=0. This contrasts with the classical case of image where the only indecomposable torsion free cotorsion groups are image, and the groups of all p-adic integers for each prime p.