Extension conjecture for automorphisms of plane-curve complements

Let $C\subset\mathbb{P}^2_{\mathbb{C}}$ be an irreducible curve. A curve is of type I if there exists a point $a\in C$ such that $C\backslash a$ is isomorphic to the affine line; a nodal cubic curve is a cubic plane curve with a node. Extension conjecture. If $C$ is neither of type I nor a nodal cubic curve, then every automorphism of the affine surface $\mathbb{P}^2\backslash C$ extends to an automorphism of $\mathbb{P}^2$. This conjecture is presented as a related problem, and the supplied text gives no resolution status.