The performance of search algorithms for grid-based pathfinding, e.g. A*, critically depends on the heuristic function that is used to focus the search. Recent studies have shown that informed heuristics that take the positions/shapes of the obstacles into account can be approximated with the deep neural networks. Unfortunately, the existing learning-based approaches mostly rely on the assumption that training and test grid maps are drawn from the same distribution (e.g., city maps, indoor maps, etc.) and perform poorly on out-of-distribution tasks. This naturally limits their application in practice when often a universal solver is needed that is capable of efficiently handling any problem instance. In this work, we close this gap by designing an universal heuristic predictor: a model trained once, but capable of generalizing across a full spectrum of unseen tasks. Our extensive empirical evaluation shows that the suggested approach halves the computational effort of A* by up to a factor of 2.2, while still providing solutions within 3% of the optimal cost on average altogether on the tasks that are completely different from the ones used for training $\unicode{x2013}$ a milestone reached for the first time by a learnable solver.