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We consider 1-equivariant wave maps from 1+2 dimensions to the 2-sphere offinite energy. We establish a classification of all degree 1 global solutionswhose energies are less than three times the energy of the harmonic map Q. Inparticular, for each global energy solution of topological degree 1, we showthat the solution asymptotically decouples into a rescaled harmonic map plus aradiation term. Together with our companion article, where we consider the caseof finite-time blow up, this gives a characterization of all 1-equivariant,degree 1 wave maps in the energy regime [E(Q), 3E(Q)).

Characterization of large energy solutions of the equivariant wave map problem: II