  We give a method for taking microscopic limits of normal matrix ensembles. We
apply this method to study the behaviour near certain types of singular points
on the boundary of the droplet. Our investigation includes ensembles without
restrictions near the boundary, as well as hard edge ensembles, where the
eigenvalues are confined to the droplet. We establish in both cases existence
of new types of determinantal point fields, which differ from those which can
appear at a regular boundary point, or in the bulk.
