  We analyze the asymptotic behavior of a $2$-dimensional integral current
which is almost minimizing in a suitable sense at a singular point. Our
analysis is the second half of an argument which shows the discreteness of the
singular set for the following three classes of $2$-dimensional currents: area
minimizing in Riemannian manifolds, semicalibrated and spherical cross sections
of $3$-dimensional area minimizing cones.
