Component potential modeling based on solid-oxide electrochemistry is used to study a single-particle configuration where a hemispherical LSM particle sits on a YSZ electrolyte half-space. The primary comparison is between two pathways: one where oxide ions travel on the particle surface; the other where these ions travel through the bulk particle interior. The systems that model each of the pathways are analyzed both mathematically and numerically, yielding insights into diffusion-reaction-conduction processes for this single-particle model. A broad range of parameter values are considered, particularly in regards to the least well-established value, the surface conductance for the surface pathway. This work includes a number of case studies that indicate which pathway dominates for a variety of parameter choices.