The role of dimensionality (Euclidean vs. fractal), spatial extent, boundary e ects and system topology on the e ciency of di usion-reaction processes involving two simultaneously di using reactants is analyzed. We present numerically exact values for the mean time to reaction, as gauged by the mean walklength before reactive encounter, obtained via application of the theory of ÿnite Markov processes, and via Monte Carlo simulation. As a general rule, we conclude that for su ciently large systems, the e ciency of di usion-reaction processes involving two synchronously di using reactants (two-walker case) relative to processes in which one reactant of a pair is anchored at some point in the reaction space (one-walker plus trap case) is higher, and is enhanced the lower the dimensionality of the system. This di erential e ciency becomes larger with increasing system size and, for periodic systems, its asymptotic value may depend on the parity of the lattice. Imposing conÿning boundaries on the system enhances the di erential eciency relative to the periodic case, while decreasing the absolute e ciencies of both two-walker and one-walker plus trap processes. Analytic arguments are presented to provide a rationale for the results obtained. The insights a orded by the analysis to the design of heterogeneous catalyst systems is also discussed.