  We use hyperbolic towers to answer some model theoretic questions around the
generic type in the theory of free groups. We show that all the finitely
generated models of this theory realize the generic type $p_0$, but that there
is a finitely generated model which omits $p_0^{(2)}$. We exhibit a finitely
generated model in which there are two maximal independent sets of realizations
of the generic type which have different cardinalities. We also show that a
free product of homogeneous groups is not necessarily homogeneous.
