Minimum-semidegree conjecture for bounded-degree spanning oriented trees

Let $\Delta\in\mathbb N$, and let $c$ be a constant. The bounded-degree spanning-tree conjecture. For every $\Delta$ there is a $c$ such that every sufficiently large $n$-vertex digraph with minimum semidegree at least $n/2+c\log n$ contains every $n$-vertex oriented tree of maximum total degree at most $\Delta$. This is presented as a missing directed analogue of a graph theorem and remains open.