Localised structures are given by some structures together with an independence relation. They are meant to encode the notion of “locality” in Physics. Taking into account locality allows to define a (multivariate) regularisation of branched zeta values. Branched zeta values are a generalization of the usual zeta values in the same way that decorated rooted trees are a generalization of words. The construction of the branched zeta values uses a universal property of rooted trees decorated by a localised set.