  We obtain some properties of $C^1$ generic surface diffeomorphisms as
finiteness of {\em non-trivial} attractors, approximation by diffeomorphisms
with only a finite number of {\em hyperbolic} homoclinic classes, equivalence
between essential hyperbolicity and the hyperbolicity of all {\em dissipative}
homoclinic classes (and the finiteness of spiral sinks). In particular, we
obtain the equivalence between finiteness of sinks and finiteness of spiral
sinks, abscence of domination in the set of accumulation points of the sinks,
and the equivalence between Axiom A and the hyperbolicity of all homoclinic
classes. These results improve \cite{A}, \cite{a}, \cite{m} and settle a
conjecture by Abdenur, Bonatti, Crovisier and D\'{i}az \cite{abcd}.

Dynamical Systems