Freeman’s centralization (Freeman, 1978) for a given centrality index is a measure of how central a vertex is regarding to how central all the other vertices are with respect to the given index. The transmission of a vertex in a graph is equal to the sum of distances between and all other vertices of . In this paper we study the centralization of transmission, in particular, we determine the graphs on vertices which attain the maximum or minimum value. Roughly, the maximizing graphs are comprised of a path which has one end glued to a clique of similar order. The minimizing family of extremal graphs consists of three paths of almost the same length, glued together in one end-vertex. We conclude the paper with some problems for possible further work.