An offensive -alliance in a graph is a set of vertices with the property that every vertex in the boundary of has at least more neighbors in than it has outside of . An offensive -alliance is called global if it forms a dominating set. In this paper we study the problem of partitioning the vertex set of a graph into (global) offensive -alliances. The (global) offensive -alliance partition number of a graph , denoted by () , is defined to be the maximum number of sets in a partition of such that each set is an offensive (a global offensive) -alliance. We show that if is a graph without isolated vertices and . Moreover, we show that if is partitionable into global offensive -alliances for , then . As a consequence of the study we show that the chromatic number of is at most 3 if . In addition, for , we obtain tight bounds on and in terms of several parameters of the graph including the order, size, minimum and maximum degree. Finally, we study the particular case of the cartesian product of graphs, showing that , for , where denotes the maximum degree of , and , for .