  We study the following problem introduced by Dujmovic et al. Given a tree $T
= (V,E)$, on $n$ vertices, a set of $n$ lines $\mathcal{L}$ in the plane and a
bijection $\iota: V \rightarrow \mathcal{L}$, we are asked to find a
crossing-free straight-line embedding of $T$ so that $v\in \iota(v)$, for all
$v\in V$. We say that a set of $n$ lines $\mathcal{L}$ is universal for trees
if for any tree $T$ and any bijection $\iota$ there exists such an embedding.
We prove that any sufficiently big set of lines is not universal for trees,
which solves an open problem asked by Dujmovic et al.
