In 2000, Vojta solved the n-squares problem under the Bombieri-Lang conjecture, by explicitly finding all the curves of genus 0 or 1 on the surfaces related to this problem. The fundamental notion used by him is omega-integrality of curves. In this talk, I will show a generalization of Vojta's method to find all curves of low genus in some surfaces, with arithmetic applications. I will also explain how to use omega-integrality to obtain a bound of the height of a non-constant morphism from a curve to the projective plane in terms of the number of intersections (without multiplicities) of its image with a divisor of a particular kind. This proves some new special cases of Vojta's conjecture for function fields.