On the number of rational points on special families of curves over   function fields
  We construct families of curves which provide counterexamples for a uniform boundedness question. These families generalize those studied previously by several authors. We show, in detail, what fails in the argument of Caporaso, Harris, Mazur that uniform boundedness follows from the Lang conjecture. We also give a direct proof that these curves have finitely many rational points and give explicit bounds for the heights and number of such points. 
Douglas Ulmer and Jos\'e Felipe Voloch
math.NT