The Diadochi (Gk. Diadochoi, Lat. Diadochi) are the successors of Alexander the Great. . . . Since Alexander had no suitable heir, his generals struggled to gain his throne and the initial arrangement for the administration of the empire, the so-called Babylon settlement, did not last long. The most important of the Diadochi were Antipater and his son Cassander, Antigonus Monophthalmus and his son Demetrius Poliorcetes, Craterus, Eumenes, Leonnatus, Lysimachus, Perdiccas, Ptolemy and Seleucus.
Alexander had no true successor, as none of the generals was able to defeat all his rivals and acquire the entire realm. Antigonus Monophthalmus came closest. Scholarly consensus holds that some of the Diadochi, especially Cassander and Ptolemy, never aimed at universal rule, but were prepared to settle with part of Alexander’s legacy. Nonetheless, it is not really accurate to say that the Successors divided the empire; it rather fell apart because they all wanted to eliminate all their rivals but none of them achieved this. (
http://www.ancientlibrary.com/wcd/Diadochi)