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The poset of copies of a relational structure ${\mathbb X}$ is the partialorder ${\mathbb P} ({\mathbb X} ) := \langle \{ Y \subset X: {\mathbb Y} \cong{\mathbb X}\}, \subset \rangle$ and each similarity of such posets (e.g.isomorphism, forcing equivalence) determines a classification of structures. Weconsider the countable ultrahomogeneous tournaments: ${\mathbb Q} $ (therational line), ${\mathbb S} (2)$ (the circular tournament), and ${\mathbb T}^\infty$ (the random tournament); as well as the ultrahomogeneous digraphs${\mathbb S} (3)$, ${\mathbb Q} [{\mathbb I}_n]$, ${\mathbb S} (2)[{\mathbbI}_n]$ and ${\mathbb T} ^\infty [{\mathbb I}_n]$ from Cherlin's list.  If ${\mathbb G} _{{\mathrm{Rado}}}$ (resp. ${\mathbb Q} _n$) denotes thecountable homogeneous universal graph (resp. $n$-labeled linear order), itturns out that ${\mathbb P} ({\mathbb T} ^\infty)\cong {\mathbb P} ({\mathbbG}_{{\mathrm{Rado}}})$ and that ${\mathbb P} ({\mathbb Q} _n)$ densely embedsin ${\mathbb P} ({\mathbb S} (n))$, for $n\in\{ 2,3\}$.  Consequently, ${\mathbb B} _{\mathbb X} \cong {\mathrm{ro}}\, ({\mathbb S}\ast \pi)$, where ${\mathbb S}$ is the Sacks forcing and $1_{\mathbb S} \Vdash"\pi $ is a separative, atomless and $\sigma$-closed forcing", whenever${\mathbb X}$ is a countable structure equimorphic with ${\mathbb Q}$,${\mathbb Q} _n$, ${\mathbb S} (2)$, ${\mathbb S} (3)$, ${\mathbb Q} [{\mathbbI}_n]$ or ${\mathbb S} (2)[{\mathbb I}_n]$.  Also, ${\mathbb B} _{\mathbb X} \cong {\mathrm{ro}}\, ({\mathbb S} \ast\pi)$, where $1_{\mathbb S} \Vdash "\pi $ is an $\omega$-distributive forcing",whenever ${\mathbb X}$ is a countable graph embedding ${\mathbb G}_{{\mathrm{Rado}}}$, or a countable tournament embedding ${\mathbb T} ^\infty$,or ${\mathbb X} ={\mathbb T} ^\infty [{\mathbb I}_n]$.

Posets of Copies of Countable Ultrahomogeneous Tournaments