A spanning tree of a finite connected graph G is a connected subgraph of G that contains every vertex and no cycles. A well-known way to generate a uniform spanning tree (UST) is the Aldous-Broder algorithm. This is a stochastic process with values in rooted trees that is driven by a random walk on G and converges as time goes to infinity towards the Brownian Continuum Tree (CRT). On the complete graph it is known that this process has a GH-scaling limit which is referred to as Root Growth with Regrafting dynamics (RGRG). We will show that this is again a universal phenomenon, i.e., it holds for the Alous-Broder chain on any appropriate sequence of regular graphs in the transient regime. In particular, this holds for the torus in dimensions five and higher. This is joint work with Osvaldo Angtuncio Hernandez and Gabriel Berzunza Ojeda.