Damn: I just noticed my note got the map $p: \tilde{G} \to G$ the wrong way round, though I am sure the correction was spotted easily. I should also say that aim of the Brown-Mucuk paper (again following Pradines) is to use methods of free groupoids to get the monodromy principle as well: the globalisation of local morphisms to the star universal cover. The nice point is that if (G,W) is a locally Lie groupoid one gets star covering morphisms \tilde G \to Hol(G,W) \to G, and there may be interesting Lie groupoids sandwiched between the first two. There is a problem of terminology. From a topological groupoid G one obtains a groupoid $\tilde{G}$ which is the star universal cover. If $G = X \times X$, then \tilde G is the fundamental groupoid of X. If G is the equivalence relation of a foliation, then \tilde G is the socalled ``homotopy groupoid'' of the foliation, i.e. the fundamental groupoid of X with the leaf topology. There is a temptation to call \tilde G the ``fundamental groupoid of G'', but this conflicts with the fundamental groupoid of the underlying space of (the arrows of ) G. Ronnie +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++