  This paper, which is the second of a series of three papers, studies
dynamical properties of elements of $\mathrm{Out}(F_{\tt n})$, the outer
automorphism group of a nonabelian free group $F_{\tt n}$. We prove that, for
every exponentially growing outer automorphism of $F_{\tt n}$, there exists a
preferred compact topological space, the space of currents relative to a
malnomal subgroup system, on which $\phi$ acts by homeomorphism with a
North-South dynamics behavior.
