We consider a uniform spanning tree under an n-arm event. The total winding of the branches has an exact asymptotic formula, which involves the Brownian loop measure and -- interestingly -- depends on the total number of branches only through its parity. Not surprisingly, the branches converge to multiradial SLE(2), and the law of the hitting points of the branches to the boundary coincides with that of eigenvalues of an COE random matrix.

Joint work with Nathanael Berestycki, Marcin Lis, and Mingchang Liu.