The fundamental properties of steep neoclassical plasma pedestals in a quiescent tokamak plasma have been investigated with a new guiding center particle code XGC: an X-point included Guiding Center code. It is shown that the width of the steepest neoclassical pedestals is similar to an experimentally observed edge pedestal width, and that a steep pedestal must be accompanied by a self-consistent negative radial electric field well. It is also shown that a steep neoclassical pedestal can form naturally at a quiescent diverted edge as the particle source from the neutral penetration (and heat flux from the core plasma) is balanced by the sharply increasing convective ion loss toward the separatrix. The steep neoclassical pedestal and the strong radial electric field well are suppressed by an anomalous diffusion coefficient of a strength appropriate to an L-mode state; nonetheless, the ExB shearing rate increases rapidly with pedestal temperature. Additionally, the present study shows that a steep pedestal at the diverted edge acts as a cocurrent parallel momentum source. (C) 2004 American Institute of Physics.