  In the present work we establish a quantization result for the angular part
of the energy of solu- tions to elliptic linear systems of Schr\"odinger type
with antisymmetric potentials in two dimension. This quantization is a
consequence of uniform Lorentz-Wente type estimates in degenerating annuli. We
derive from this angular quantization the full energy quantization for general
critical points to functionals which are conformally invariant or also for
pseudo-holomorphic curves on degenerating Riemann surfaces.
