We introduce and examine a class of stochastic spatial point processes with births and deaths, related to spatial loss networks introduced in . In these processes, a point stays in the system until it is removed due to interaction with a conflicting new arrival. In particular, we consider an interaction scheme where two points are conflicting if closed balls of radius 1 2 around them overlap and a new arriving point "kills" each conflicting point independently with probability ρ. The new point is accepted if all conflicting points are killed. We construct this process on the whole Euclidean space Rd. If ρ is large enough, we show existence of a stationary regime and exponential convergence to the stationary distribution. Such stochastic models have been studied earlier as models for populations of interacting individuals or as spatial queuing and resource sharing networks.