  We explore the birational structure and invariants of a foliated surface $(X,
\mathcal F)$ in terms of the adjoint divisor $K_{\mathcal F}+\epsilon K_X$, $0<
\epsilon \ll 1$. We then establish a bound on the automorphism group of an
adjoint general type foliated surface $(X, \mathcal F)$, provide a bound on the
degree of a general curve invariant by an algebraically integrable foliation on
a surface and prove that the set of $\epsilon$-adjoint canonical models of
foliations of general type and with fixed volume form a bounded family.
