  The main theorem of this paper generalizes recent results in Dehn surgery to
the case of handlebody attachment. We consider attaching handlebodies and solid
tori to the boundary of an irreducible, boundary-irreducible, atoroidal and
acylindrical 3-manifold. We show that for a large class of homeomorphisms
attaching these handlebodies, the fundamental group of the resulting manifold
contains the fundamental group of a closed surface of genus at least two.
