  We consider categories of relational structures that fully embed every
category of universal algebras, and prove a partial characterisation of these
in terms of an infinitary variant of the notion of nowhere density of
Ne\v{s}et\v{r}il and Ossona de Mendez. More precisely, we show that the Gaifman
class of an algebraically universal category contains subdivided complete
graphs of any infinite size, and establish that any monotone category
satisfying this may be oriented to obtain an algebraically universal category.
For the proof of the above, we also develop a categorical framework for
relational gadget constructions. This generalises known results about
categories of finite graphs to categories of relational structures of unbounded
size.
