Alternatives to the usual picture of advanced tokamak (AT) discharges are those that form when anomalous effects alter the plasma current and pressure profiles and those that achieve stationary characteristics through mechanisms so that 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 {approx} 1 and those with a deeply hollow current channel and high values of q. Operating scenarios with high fusion performance at low current and where the inductively driven current density achieves a stationary configuration with either small or non-existing sawteeth may enhance the neutron fluence per pulse on ITER and future burning plasmas. Hollow current profile discharges exhibit high confinement and a strong ''box-like'' internal transport barrier (ITB). We present results providing evidence for current profile formation and evolution exhibiting features consistent with anomalous effects or with self-organizing mechanisms. Determination of the underlying physical processes leading to these anomalous effects is important for scaling of current experiments for application in future burning plasmas
