Alternatives to the usual picture of advanced tokamak (AT) discharges are those that form when anomalous thermal conductivity and/or resistivity alter plasma current and pressure profiles to achieve stationary characteristics through self-organizing mechanisms where a measure of desired AT features is maintained without external current-profile control. Regimes exhibiting these characteristics are those where the safety factor (q) evolves to a stationary profile with the on-axis and minimum q~ 1. Operating scenarios with fusion performance exceeding H-mode at the same plasma current and where the inductively driven current density achieves a stationary configuration with either small or nonexisting sawteeth should enhance the performance of ITER and future burning plasma experiments. We present simulation results of anomalous current-profile formation and evolution using theory-based hyper-resistive models. These simulations are stimulated by experimental observations with which we compare and contrast the simulated evolution. We find that the hyper-resistivity is sufficiently strong to modify the current-profile evolution to achieve conditions consistent with experimental observations. Modelling these anomalous effects is important for developing a capability to scale current experiments to future burning plasmas.