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Let ${\mathcal U}_{\delta}$ be the uniform spanning tree on $\delta\mathbb{Z}^{3}$. A spanning cluster of ${\mathcal U}_{\delta}$ is a connectedcomponent 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 rightface $\{ 1 \} \times [0,1]^{2}$. In this note, we will prove that the number ofthe spanning clusters is tight as $\delta \to 0$, which resolves an openquestion raised by Benjamini (1999).

The number of spanning clusters of the uniform spanning tree in three dimensions