This paper investigates a distributed connectivity-preserving and collision-avoiding formation tracking problem of networked uncertain underactuated surface vessels (USVs) with heterogeneous limited communication ranges. All nonlinearities in the dynamic model are assumed to be completely unknown. Compared with the existing formation tracking results for USVs, our primary contribution is to develop a new nonlinearly transformed formation error for achieving the initial connectivity preservation, the collision avoidance, and the distributed formation tracking without switching the desired formation pattern and using any additional potential functions. In other words, these three objectives can be achieved by using only one transformed formation error surface. The local tracker design strategy using the nonlinearly transformed error is established under the direct graph topology, where the adaptive function approximation technique and the auxiliary variables are employed to compensate for uncertain nonlinearities and to deal with the underactuated problem of USVs, respectively. Finally, the Lyapunov stability analysis and simulations are performed to verify the effectiveness of the proposed theoretic result.