Let $T$ be a locally finite simplicial tree andlet $\Gamma\subset{\rm Aut}(T)$ be a finitely generated discrete subgroup. Weobtain an explicit formula for the critical exponent of the Poincaréseriesassociated with $\Gamma$, which is also the Hausdorff dimension of the limitset of $\Gamma$; this uses a description due to Lubotzky of anappropriate fundamental domain for finite index torsion-free subgroupsof $\Gamma$.Coornaert, generalizing work of Sullivan, showed thatthe limit set is of finite positive measure in its dimension; we give a newproof of this result. Finally, we show that the critical exponent is locallyconstant on the space of deformations of$\Gamma$.