Earth scientists have traditionally conceptualized rivers and streams as geomorphic machines, whose role is to transfer sediment and to sculpt the landscape. Steady-state relationships between sediment supply and transport capacity have traditionally been considered normative in fluvial systems. Rivers are hydrological entities, however, whose function is to redistribute excess moisture on land. The geomorphic work of the river – erosion, transport, deposition, etc. – is a byproduct of the hydrological job of the river. There is therefore no reason to expect any particular relationship between sediment supply and transport capacity to develop as a normative condition in fluvial systems. The apparent steady-state equilibrium slope adjustments of rivers are a byproduct of four basic phenomena: (1) hydraulic selection, which favors channels and branching networks over other flux patterns; (2) water flows along the available path of least resistance; (3) energy dissipation; and (4) finite relaxation times. Recognizing converging trends of stream power or slope and sediment supply as common (but far from inevitable) side effects rather than self-regulation has important implications for interpreting and predicting fluvial systems, and for river management and restoration. Such trends are variable, transient, contingent, and far from universal. Where they occur, they are an emergent byproduct of fundamental physical mechanisms, not a goal function or attractor state. Copyright © 2009 John Wiley & Sons, Ltd.