  The $abc$ conjecture predicts a highly non trivial upper bound for the height
of an algebraic point in terms of its discriminant and its intersection with a
fixed divisor of the projective line counted without multiplicity. We describe
the two independent proofs of the strong $abc$ conjecture over function fields
given by McQuillan and Yamanoi. The first proof relies on tools from
differential and algebraic geometry; the second relies on analytic and
topological methods. They correspond respectively to the Nevanlinna and the
Ahlfors approach to the Nevanlinna Second Main Theorem.
