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In this paper, we propose GOHOME, a method leveraging graph representations of the High Definition Map and sparse projections to generate a heatmap output representing the future position probability distribution for a given agent in a traffic scene. This heatmap output yields an unconstrained 2D grid representation of agent future possible locations, allowing inherent multimodality and a measure of the uncertainty of the prediction. Our graph-oriented model avoids the high computation burden of representing the surrounding context as squared images and processing it with classical CNNs, but focuses instead only on the most probable lanes where the agent could end up in the immediate future. GOHOME reaches 2$nd$ on Argoverse Motion Forecasting Benchmark on the MissRate$_6$ metric while achieving significant speed-up and memory burden diminution compared to Argoverse 1$^{st}$ place method HOME. We also highlight that heatmap output enables multimodal ensembling and improve 1$^{st}$ place MissRate$_6$ by more than 15$\%$ with our best ensemble on Argoverse. Finally, we evaluate and reach state-of-the-art performance on the other trajectory prediction datasets nuScenes and Interaction, demonstrating the generalizability of our method.