  In equilibrium planer systems of Hall electrons, such as GaAs
heterostructures and graphene, support two species of current counterflowing
along the system edges, as observed recently in experiment using a nanoscale
magnetometer. We examine distinct origins and distinctive features of these
equilibrium currents, with the Coulombic many-body effects taken into account,
and derive their real-space distributions. Our basic tool of analysis is a
reformulation of quantum Hall systems as a W_{infinity} gauge theory, which
allows one to diagonalize the total Hamiltonian according to the resolutions of
external probes. These equilibrium currents are deeply tied to the orbital
magnetization in quantum Hall systems. Special attention is drawn to the case
of graphene, especially the neutral (nu=0) ground state and its intrinsic
diamagnetic response that combines with the equilibrium currents to govern the
orbital magnetization and its oscillations with filling.
