Summary: We study the limiting behavior as \(|x|\rightarrow \infty\) of extremal functions \(u\) for Morrey’s inequality on \(\mathbb{R}^n\). In particular, we compute the limit of \(u(x)\) as \(|x|\rightarrow \infty\) and show |\(x|| Du (x)\)| tends to 0. To this end, we exploit the fact that extremals are uniformly bounded and that they each satisfy a PDE of the form \(-\Delta_pu=c(\delta_{x_0}-\delta_{y_0})\) for some \(c\in \mathbb{R}\) and distinct \(x_0\), \(y_0\in \mathbb{R}^n\). More generally, we explain how to quantitatively deduce the asymptotic flatness of bounded \(p\)-harmonic functions on exterior domains of \(\mathbb{R}^n\) for \(p>n\).