Fixed measure scaling limits of Christoffel--Darboux kernels encode information about orthogonal polynomials, such as the local distribution of their zeros. Different limit kernels are associated with different universality classes, e.g. sine kernel with bulk universality and locally uniform zero spacing. We will describe necessary and sufficient conditions for a class of scaling limits corresponding to homogeneous de Branges spaces; this includes bulk universality, hard edge universality, and other notable classes. The talk is based on joint work with Benjamin Eichinger and Harald Woracek.