  Let ${\mathcal U}_{\delta}$ be the uniform spanning tree on $\delta
\mathbb{Z}^{3}$. A spanning cluster of ${\mathcal U}_{\delta}$ is a connected
component of the restriction of ${\mathcal U}_{\delta}$ to the unit cube
$[0,1]^{3}$ that connects the left face $\{ 0 \} \times [0,1]^{2}$ to the right
face $\{ 1 \} \times [0,1]^{2}$. In this note, we will prove that the number of
the spanning clusters is tight as $\delta \to 0$, which resolves an open
question raised by Benjamini (1999).
