A digraph $H$ is called ubiquitous if every digraph that contains $k$ disjoint copies of $H$ for every $k \in \mathbb{N}$ also contains infinitely many disjoint copies of $H$. We study oriented double rays, that is digraphs $H$ whose underlying undirected graphs are double rays. We characterise which oriented double rays are ubiquitous with the exception of the consistently oriented double ray.
Comment: 11 pages, 1 figure