In the context of parametric surrogates, several nontrivial issues arise when a whole curve shall be predicted from given input features. For instance, different sampling or ending points lead to non-aligned curves. This also happens when the curves exhibit a common pattern characterized by critical points at shifted locations (e.g., in mechanics, the elasticplastic transition or the rupture point for a material). In such cases, classical interpolation methods fail in giving physics-consistent results and appropriate pre-processing steps are required. Moreover, when bifurcations occur into the parametric space, to enhance the accuracy of the surrogate, a coupling with clustering and classification algorithms is needed. In this work we present several methodologies to overcome these issues. We also exploit such surrogates to quantify and propagate uncertainty, furnishing parametric stastistical bounds for the predicted curves. The procedures are exemplified over two problems in Computational Mechanics.