The work presents an investigation of turbulent propane flames stabilized by planar injection across the span of a square cylinder, either from its leading face against the approach flow or directly into its vortex formation region. The non-premixed or partially premixed reacting wakes were studied by regulating the fuel injection level and position. Turbulent velocities, temperatures, CH*, flame images, and exhaust emissions were measured using laser velocimetry, digitally compensated thermocouples, chemiluminescence imaging, and gas analysis. Lean and ultra-lean fuel/air velocity ratios of 0.36 and 0.23 were investigated under concurrent and countercurrent injection at a Reynolds number, based on the square burner diameter, of 5700. Large eddy simulations were undertaken using the dynamic Smagorinsky model, the eddy dissipation concept, and an 11-step global mechanism for propane combustion and NOx. The methodology helped to elucidate some aspects regarding the interaction of the flame front with the vortex formation region, the impact of heat release on wake development, and the flame behavior as lean blow-off (LBO) was approached, under both forms of fuel injection. Differences between the partially premixed planar wake and other types of non-premixed or fully premixed configurations were also exposed and discussed. At the initial stages of fuel reduction toward blow-off, the simulations suggested a more efficient stabilization of the flanking reacting fronts within the side vortices of the counter-injected square burner by comparison to axisymmetric counterparts. However, as the two reactive layers were progressively retracted, the large scale asymmetric vortex shedding was reinstated at the flame trailing edges and had a detrimental effect on overall stability leading to a more rapid approach to LBO in the final stages.