We identify the (local) limits of the λ-spanning forest of any sequence of regular graphs with degrees going to infinity. In particular, the limits fall into three main regimes, depending on how λ is tuned with the degree parameter. The proof exploits fundamental links between uniform spanning trees and loop-erased random walks and provides an intuitive explanation of the distribution of the limit at infinity. The proof extends to sequences of ``almost-regular'' graphs. D'Achille, Enriquez, and Melotti (2026) recently proved the same result for complete graphs. This is joint work with Eleanor Archer (Université Paris Dauphine - PSL).