The talk will report on joint work with Amos Turchet on a standard conjecture of diophantine geometry usually attributed to Vojta. This conjecture predicts that the complement in the complex projective plane of a general nodal curve, B, of degree at least 4 contains finitely many copies of \(\mathbb{C}^*\), where \(\mathbb{C}^*\) is the set of nonzero complex numbers. This is equivalent to the fact that the preimage of B under any non constant map from a smooth rational curve, X, to the plane has cardinality at most 2. Via a purely geometric approach, we prove this conjecture effectively when B has at least three irreducible components, and without the rationality assumption on X.