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In this paper we prove that if $\phi:\C\to\C$ is a $K$-quasiconformal map,with $K>1$, and $E\subset \C$ is a compact set contained in a ball $B$, then$$\frac{\dot C_{\frac{2K}{2K+1},\frac{2K+1}{K+1}}(E)}{\diam(B)^{\frac2{K+1}}}\geq c^{-1} (\frac{\gamma(\phi(E))}{\diam(\phi(B))})^{\frac{2K}{K+1}},$$ where$\gamma$ stands for the analytic capacity and $\dotC_{\frac{2K}{2K+1},\frac{2K+1}{K+1}}$ is a capacity associated to a non linearRiesz potential.  As a consequence, if $E$ is not $K$-removable (i.e. removable for bounded$K$-quasiregular maps), it has positive capacity $\dotC_{frac{2K}{2K+1},\frac{2K+1}{K+1}}$. This improves previous results thatassert that $E$ must have non $\sigma$-finite Hausdorff measure of dimension$2/(K+1)$. We also show that the indices $\frac{2K}{2K+1}$, $\frac{2K+1}{K+1}$are sharp, and that Hausdorff gauge functions do not appropriately discriminatewhich sets are $K$-removable. So essentially we solve the problem of findingsharp "metric" conditions for $K$-removability.

Quasiconformal maps, analytic capacity, and non linear potentials