Abstract
In this paper we continue our investigations of Racz's parabolic-hyperbolic formulation of the Einstein vacuum constraints. Our previous studies of the asymptotically flat setting provided strong evidence for unstable asymptotics which we were able to resolve by introducing a certain modification of Racz's parabolic-hyperbolic formulation. The primary focus of the present paper here is the asymptotically hyperboloidal setting. We provide evidence through a mixture of numerical and analytical methods that the asymptotics of the solutions of Racz's parabolic-hyperbolic formulation are stable, and, in particular, no modifications are necessary to obtain solutions which are asymptotically hyperboloidal.