The Gromov density model of random groups provides a way to explore generic properties of random quotients of free groups. In particular, it is known that these groups are (at appropriate densities) hyperbolic and cubulated. In this talk we will explore a new model of random quotients of free products of groups. These groups are relatively hyperbolic and relatively cubulated with respect to their factor groups. This is joint work in progress with E Einstein, S Krishna, T Ng, and M Steenbock.