The quasi-steady state Fisher model is used to analyze the efficiency of delivery of a diffusing matter to a triple junction point in an ensemble of three intersecting grain boundaries. A version of grain boundary ensemble is considered in which two grains adjacent to a surface containing a diffusion source are at a tilt angle of 30° and the third boundary is normal to the surface. This configuration of grain boundaries corresponds to a triple junction angle of 120°. It is shown that the efficiency of delivery of a matter to the triple point depends on the ratio of the diffusion length of grain boundaries adjacent to the surface containing a diffusion source to the triple junction depth and on the relation between the grain boundary diffusion coefficients of each grain boundary in the ensemble. The conditions are found under which enhanced diffusion as compared to diffusion in a single boundary takes place in an ensemble of grain boundaries.