The author considers the problem of determining parametric maximal flows in networks with gains. Two kinds of parametrization are investigated: parametric flows leaving the source and parametric capacities of the arcs. Both characteristics are linear functions of the parameter \(\lambda\). The goal is to determine the optimal value function \(x_ t(\lambda)\) (amount of flow entering the sink t). Points at which the slope of \(x_ t(\lambda)\) changes are called breakpoints. An efficient implementation of the general piece-by-piece fashion for solving parametric linear programs (vertical approach) is given. A worst-case analysis with respect to the number of breakpoints in the optimal objective value function is performed. The result is an exponential growth of the number of breakpoints depending on the number of vertices in the underlying graph. The worst-case complexity results are the motivation for adapting the idea of a horizontal approximation method developed by H. W. Hamacher and L. R. Foulds [Z. Oper. Res. 33, No.1, 21-37 (1989] for parametric flows in pure networks to the more general case which includes flows with gains. The last algorithm is illustrated by a numerical example.