  We establish quadratic asymptotics for solutions to special Lagrangian
equations with supercritical phases in exterior domains. The method is based on
an exterior Liouville type result for general fully nonlinear elliptic
equations toward constant asymptotics of bounded Hessian, and also certain
rotation arguments toward Hessian bound. Our unified approach also leads to
quadratic asymptotics for convex solutions to Monge-Amp\`{e}re equations
(previously known), quadratic Hessian equations, and inverse harmonic Hessian
equations over exterior domains.
