  For a graph $G$, and two distinct vertices $u$ and $v$ of $G$, let $n_G(u,v)$
be the number of vertices of $G$ that are closer in $G$ to $u$ than to $v$.
Miklavi\v{c} and \v{S}parl (arXiv:2011.01635v1) define the
distance-unbalancedness of $G$ as the sum of $|n_G(u,v)-n_G(v,u)|$ over all
unordered pairs of distinct vertices $u$ and $v$ of $G$. Confirming one of
their conjectures, we show that the stars minimize the distance-unbalancedness
among all trees of a fixed order.
