Between-subject brain variability in shape and function is a major challenge to the definition of accurate brain models [1, 2]. It also obscures the comparison between species. Recently, precision mapping has started to provide data to ground the definition of accurate brain models [3]. Yet technology has been missing to identify correspondences between brains. Leveraging Optimal Transport (OT) methods [5, 6], we derive an algorithm, denoted as unbalanced fused Gromov Wasserstein (UFGW), to compute whole-brain mappings between subjects with minimal anatomical priors, and provide a fast GPU-based Python implementation. We apply it to the Individual Brain Charting dataset - a collection of more than 200 maps of functional activations (contrasts) acquired in 12 human subjects [4]. Our method focuses on building mappings for surface-sampled data. We compare UFGW with its diffeomorphic counterparts (such as Procrustes [12], MSM [7] or spherical daemon [13]). To do so, we systematically evaluate the relevance of derived mappings by (a) quantitatively assessing how well they predict unseen contrasts and (b) qualitatively looking at the cortical reorganisation they induce between subjects through a dedicated web-based interactive visualisation tool. On top of being computationally very efficient and easy to deploy, UFGW outperforms alternatives. Unlike other methods, UFGW doesn’t enforce diffeomorphicity between source and target surfaces, but only fosters it. This makes it possible to capture subtle changes between individuals, such as the size and shape of functional areas or their position relative to other areas. Our visualisation tool facilitates exploring these changes. Moreover, as our method is not based on anatomical landmarks, it is particularly suited for cross-species comparisons (e.g. human vs. macaques). We plan to derive these in future work to assess the existence of cortical reorganisations between species, pushing forward recent efforts made in cross-species comparisons [8, 9, 10].