Many industrial processes elongate polymer liquids at rates much faster than the molecular chain's characteristic relaxation times. These nonlinear elongation flows can strongly deform microscopic polymer conformations and drive dynamic transitions that produce large changes in polymer viscosity. Understanding how flow depends upon and drives such changes in polymer microstructure is essential for improving polymer processing and recycling; However, the current molecular picture of these flows has come from inferring molecular dynamics from macroscopic rheology. Recently, new molecular simulation techniques have allowed modelers to simulate and characterize the macromolecular dynamics of polymer melts during strong uniaxial elongational flows, revealing new nonequilibrium behaviors. Here, I’ll share simulation results for the uniaxial elongation of ring polymer melts and blends. Simulations reproduce the rate-dependent nonlinear rheology observed in ring experiments and reveal that it is driven by a small number of rings that spontaneously assemble into supramolecular daisy-chains. This produces a new type of outlier dominant rheology that cannot be described by average order parameters of the polymer fluid but may be a powerful tool for designing new polymer fluids.