In recent years, low dimensional topologists have become interested in the study of "generic" smooth maps to surfaces. The approach is similar to Morse theory, only with two dimensional target. In this talk, I will discuss a specific problem in the 4-dimensional context which is analogous to the (uniqueness of) cancellation of critical points of Morse functions. I will also indicate applications to certain pictorial descritpions of 4-manifolds in terms of curve configurations on surfaces. This is joint work with Kenta Hayano.