David maps are generalizations of classical planar quasiconformal maps for which the dilatation is allowed to tend to infinity in a controlled fashion. In this note we examine how these maps distort Hausdorff dimension. We show

• Given $\alpha$ and $\beta$ in $[0,2]$, there exists a David map $\varphi:\mathbb {C} \to \mathbb {C}$ and a compact set $\Lambda$ such that $\operatorname{dim}_{\operatorname{H}} \Lambda =\alpha$ and $\operatorname{dim}_{\operatorname{H}} \varphi(\Lambda)=\beta$.
• There exists a David map $\varphi:\mathbb {C} \to \mathbb {C}$ such that the Jordan curve $\Gamma=\varphi ({\mathbb  S}^1)$ satisfies $\operatorname{dim}_{\operatorname{H}} \Gamma=2$.

One should contrast the first statement with the fact that quasiconformal maps preserve sets of Hausdorff dimension $0$ and $2$. The second statement provides an example of a Jordan curve with Hausdorff dimension $2$ which is (quasi)conformally removable.