We explore two-dimensional, steady state, flow and thermal models of oceanic spreading center structure. These models include the effects of hydrothermal heat transport and crustal accretion for two basic accretion geometries: (1) a lens model where all crust below the sheeted dike layer passes through a magma lens at the base of the dike layer before subsiding and flowing to deeper levels; and (2) a dike model where crust is emplaced in a vertical slot from the surface to Moho and subsequently moves horizontally (rigidly) away from the axis of accretion. The axial heat flux resulting from these two end-member accretion geometries is compared, and an assessment is made of the feasibility of using various observations to differentiate between these two accretion geometries. We find that the steady state axial heat flux is predominantly influenced by three factors: the spreading rate, the magmatic budget (crustal thickness) and the efficiency of hydrothermal cooling. The total steady state heat flux from the neovolcanic zone (2 km wide) increases almost linearly with the spreading rate for both the dike and lens accretion geometries. The major difference between the dike and the lens models is nonthermal: they predict different accumulated strain distributions within off-axis crust. Crustal flow due to crustal accretion within a crustal-height ''dike'' leads to little accumulated strain, while intense crustal strain results from crustal subsidence and flow below a steady state magma lens. Ophiolite and marine seismic observations of crustal layering appear to be the strongest observational tests to discriminate between these two accretion geometries; they currently favor a lens-like model of lower crustal accretion. ¿ American Geophysical Union 1996