Let ${(e_{\beta }:𝐐\to Y_{\beta })}_{\beta \in \mathbf{\text{Ord}}}$ be the large source of epimorphisms in the category $\mathbf{\text{Ury}}$ of Urysohn spaces constructed in [2]. A sink ${(g_{\beta }:Y_{\beta }\to X)}_{\beta \in \mathbf{\text{Ord}}}$ is called natural, if $g_{\beta }\circ e_{\beta }=g_{{\beta }^{\text{'}}}\circ e_{{\beta }^{\text{'}}}$ for all $\beta ,{\beta }^{\text{'}}\in \mathbf{\text{Ord}}$. In this paper natural sinks are characterized. As a result it is shown that $\mathbf{\text{Ury}}$ permits no $(Epi,ℳ)$-factorization structure for arbitrary (large) sources.