  Motivated by its relevance for the study of perturbations of one-dimensional
voter models, including stochastic Potts models at low temperature, we consider
diffusively rescaled coalescing random walks with branching and killing. Our
main result is convergence to a new continuum process, in which the random
space-time paths of the Sun-Swart Brownian net are terminated at a Poisson
cloud of killing points. We also prove existence of a percolation transition as
the killing rate varies. Key issues for convergence are the relations of the
discrete model killing points and their Poisson intensity measure to the
continuum counterparts.
