Generalized transport models, such as Dual and Multiple Continua Models, Global Random Walk, Multirate Mass Transfer and Continuous Time Random Walk are widely used for description of anomalous transport in fractured and porous media. For these models the form of the parameter space is crucial for the most accurate description of anomalous effects as well as the mean transport phenomenon. Constraining of the parameter space is required for the proper interpretation of the physical properties taking place. In this study the Generalized Continuum Transport model is considered as a versatile tool for the parameter space selection as well as better quantification of anomalous (non-Fickian) transport. Different variants of the parameter space are applied to the GCT model and the breakthrough curves obtained from the pore-network models with strong anomalities are fitted. Flexibility of the model is demonstrated through its static and dynamic adaptivity to network structure and transport complexity. The beneficial results of the curve fitting are also compared with the classical models. It is thus demonstrated that the complexity of the model as well as the model parameters can be directly determined based on fine-scale simulations.