Two-dimensional (2-D) simulations of collisionless magnetic reconnection have demonstrated the importance of the Hall term for the structure of the diffusion region and the existence of a very thin (~c/&ohgr;pe) electron current layer and sharp density/pressure gradients on c/&ohgr;pi scales. The present work explores the effects of the third dimension (along the direction of the equilibrium current) and of an open geometry along the magnetic field direction on these 2-D structures within a fully kinetic treatment based on particle-in-cell simulations. The thin electron current layer is found to remain a 2-D structure. The electric field components Ez and E∥ in the diffusion region each possess a complex structure on the c/&ohgr;pi and c/&ohgr;pe spatial scales. The Ez fields are needed to maintain pressure balance on the ion and electron species in the current sheet, while E∥ results in nearly Alfv¿nic (for the ions) and supra-Alfv¿nic (for the electrons) flows out of the diffusion region. The Hall-generated quadrupolar By field extends to large distances away from the neutral line and is a characteristic signature of collisionless reconnection. No evidence is found for the development of small-scale turbulent modes; the electron and ion flows are highly ballistic, and the currents and density remain sharply defined. The outflow region, however, can become unstable to an ideal pressure gradient instability of relatively long wavelength (kyw~0.25, where w is the half thickness of the current sheet) with the character of a kink or interchange mode. Attempts to induce localized reconnection by imposing a localized (in y) convection electric field at the asymptotic (lobe) boundaries do not alter appreciably the basic 2-D configuration. ¿ 2001 American Geophysical Union