The uniform spanning forest (USF) in Zd is the weak limit of random, uniformly chosen, spanning trees in [−n, n]d . Pemantle [11] proved that the USF consists . of a single tree if and only if d ≤ 4. We prove that any two components of the USF in Zd are adjacent . if 5 ≤ d ≤ 8, but not if d ≥ 9. More generally, let N (x, y) be the minimum number of edges outside the USF in a path joining x and y in Zd . Then max N (x, y) : x, y ∈ Zd = (d − 1)/4 .