Giant Spider Conjecture for directed and oriented graphs

For integers $k\geq 2$ and $\ell\geq 1$, a $(k,\ell)$-spider is the $(k-1)$-subdivision of an in-star with $\ell$ leaves. A directed graph is considered with its minimum out-degree, and an oriented graph is a directed graph with at most one orientation of each underlying edge. Giant Spider Conjecture. Every directed graph with minimum out-degree at least $k\ell$ and every oriented graph with minimum out-degree at least $k\ell/2$ contains a $(k,\ell)$-spider as a subgraph. The conjecture concerns the threshold at which these spiders become unavoidable under minimum out-degree conditions and remains open.