  Let (S, B) be the log pair associated with a projective completion of a
smooth quasi-projective surface V . Under the assumption that the boundary B is
irreducible, we obtain an algorithm to factorize any automorphism of V into a
sequence of simple birational links. This factorization lies in the framework
of the log Mori theory, with the property that all the blow-ups and
contractions involved in the process occur on the boundary. When the completion
S is smooth, we obtain a description of the automorphisms of V which is
reminiscent of a presentation by generators and relations except that the
"generators" are no longer automorphisms. They are instead isomorphisms between
different models of V preserving certain rational fibrations. This description
enables one to define normal forms of automorphisms and leads in particular to
a natural generalization of the usual notions of affine and Jonquieres
automorphisms of the affine plane. When V is affine, we show however that
except for a finite family of surfaces including the affine plane, the group
generated by these affine and Jonquieres automorphisms, which we call the tame
group of V, is a proper subgroup of Aut(V).
