The morphology of dark matter annihilation/decay signals offers a handle for discrimination of dark matter against astrophysical backgrounds. Recent advances in N-body simulations allow us to map out the expected distribution of morphological parameters, rather than focusing on a small sample of halos which are assumed to be representative. In this talk, I will use data from the Illustris simulation to present an analysis of the expected morphology of dark matter annihilation and decay signals, either originating from the Galactic Center or from halos other than our own. I will discuss how these expectations, and those for simulated gas and stars, compare to observations of astrophysical background emission and hints of potential signals.