Title: On Single-environment Extrapolations in Graph Classification and Regression Tasks. Abstract: Extrapolation in graph classification/regression remains an underexplored area of an otherwise rapidly developing field. Our work contributes to a growing literature by providing the first systematic counterfactual modeling framework for extrapolations in graph classification/regression tasks. To show that extrapolation from a single training environment is possible, we develop a connection between certain extrapolation tasks on graph sizes and Lovasz's characterization of graph limits. For these extrapolations, standard graph neural networks (GNNs) will fail, while classifiers using induced homomorphism densities succeed, but mostly on unattributed graphs. Generalizing these density features through a GNN subgraph decomposition allows them to also succeed in more complex attributed graph extrapolation tasks. Finally, our experiments validate our theoretical results and showcase some shortcomings of common (interpolation) methods in the literature.