Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups

Let $K$ be the function field of a curve $C$ over $\mathbb{F}$ either odd or zero characteristic. Following work by Serre and Mason on $\mathrm{SL}_2$, we study action arithmetic subgroups $\mathrm{SU}(3)$ its corresponding Bruhat-Tits tree associated to suitable completion $K$. More precisely, prove that quotient graph "looks like spider", in sense it is union set cuspidal rays (the "legs"), parametrized an explicit Picard group, are attached connected "body"). We use this description order describe these as amalgamated products their homology. In case where finite field, result Bux, K\"ohl Witzel "body" graph, which allows us get even more precise applications.