  The general problem which initiated this work is:
  What are the quasiprojective varieties which can be uniformized by means of
bounded domains in $\cz^n$ ?
  Such a variety should be, in particular, C--hyperbolic, i.e. it should have a
Carath\'{e}odory hyperbolic covering. We study here the plane projective curves
whose complements are C--hyperbolic. For instance, we show that most of the
curves whose duals are nodal or, more generally, immersed curves, belong to
this class. We also give explicit examples of irreducible such curves of any
even degree d greater or equal 6.
