  The purpose of this paper is to build an algebraic framework suited to
regularise branched structures emanating from rooted forests and which encodes
the locality principle. This is achieved by means of the universal properties
in the locality framework of properly decorated rooted forests. These universal
properties are then applied to derive the multivariate regularisation of
integrals indexed by rooted forests. We study their renormalisation, along the
lines of Kreimer's toy model for Feynman integrals.
