  We prove that posets of bounded height whose cover graphs belong to a fixed
class with bounded expansion have bounded dimension. Bounded expansion,
introduced by Ne\v{s}et\v{r}il and Ossona de Mendez as a model for sparsity in
graphs, is a property that is naturally satisfied by a wide range of graph
classes, from graph structure theory (graphs excluding a minor or a topological
minor) to graph drawing (e.g. graphs with bounded book thickness). Therefore,
our theorem generalizes a number of results including the most recent one for
posets of bounded height with cover graphs excluding a fixed graph as a
topological minor. We also show that the result is in a sense best possible, as
it does not extend to nowhere dense classes; in fact, it already fails for
cover graphs with locally bounded treewidth.
