  We compute the spectral function of a spin S hole injected into a
two-dimensional antiferromagnet or superconductor in the vicinity of a magnetic
quantum critical point. We show that, near van Hove singularities, the problem
maps onto that of a static vacancy carrying excess spin S. The hole creation
operator is characterized by a new boundary anomalous dimension and a vanishing
quasiparticle residue at the critical point. We discuss possible relevance to
photoemission spectra of cuprate superconductors near the anti-nodal points.
