  We construct a branched center manifold in a neighborhood of a singular point
of a $2$-dimensional integral current which is almost minimizing in a suitable
sense. Our construction is the first 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.
