Alexander IV (323-310): son of Alexander the Great.
Still, he may have been a bit disappointed. During the first meeting of the Macedonian generals, he had proposed not to choose a king, but to wait (text). After all, queen Roxane, an Iranian lady, was pregnant, and if she bore a son, he was the best successor. Of course, this would have given Perdiccas even more power, but he met too much resistance to reach this aim. Not many Macedonians wanted to serve a halfblood king. Not much later, Roxane gave birth to a son, who was called after his father: Alexander.
During his first years, the boy, his mother, and king Philip Arridaeus were in the company of Perdiccas, who tried to keep the empire united (First Diadoch War), but was in 320 assassinated by his officers when he was unable to defeat Ptolemy, who had made himself independent in Egypt. At Triparadisus (Baalbek?), the royal family received a new guardian, Antipater, who took the royals to Macedonia and died soon after (319).
It is not clear what Alexander's position was at this moment. Greek sources call him king, but they were all written long after the events, and it would be a constitutional novelty if Macedonia had two kings. Perhaps it is better to trust the contemporary sources from Babylonia, in which only Philip Arridaeus is called king. However this may be, as long as Alexander was a child, the real man in charge was his regent: Perdiccas, Antipater, or the man appointed by Antipater, Polyperchon.
The wisdom of this appointment has been debated, because Antipater's son Cassander felt that he had the right to be the next regent, and aligned himself with a general named Antigonus Monophtalmus, hoping that this old war horse would make him guardian of the royal family. Polyperchon now alligned himself with a former ally of Perdiccas named Eumenes, and the Second Diadoch War broke out. Alexander was now about five years old.
In the autumn of 318, Polyperchon's navy was defeated by Antigonus' fleet in the Bosphorus, and Polyperchon lost control of the Aegean Sea. Cassander benefitted: he secured the support of Athens and in the spring of 317, he was officially recognized as ruler in Macedonia and regent of Philip Arridaeus.
But not of Alexander. Polyperchon had made his escape to Epirus in the west, together with Roxane and the boy. Here, they were joined by Olympias, the mother of Alexander the Great, and king Aeacidas of Epirus. It was not a very powerful coalition, but it could play one trump card: Alexander was the lawful successor of the great Alexander, whereas Philip Arridaeus was a mere bastard of Philip.When they invaded Macedonia in October 317, Philip Arridaeus and his wife Eurydice met them at the frontier -Cassander was campaigning in the Peloponnese- but their entire army deserted them and joined the invaders. Arridaeus was immediately executed (25 December). Many supporters of Cassander were massacred as well (text).
However, Cassander was approaching and besieged Olympias in Pydna, a harbor at the foot of the holy mountain Olympus. Although both Polyperchon and Aeacidas tried to relieve her, she was forced into surrender. Cassander promised to save her life, but had her executed (early 316). Roxane and Alexander now accepted Cassander as regent, and that was the end of the Second Diadoch War in the west. Whatever Alexander's former status, he was now certainly called king.
In the east, Antigonus had defeated Eumenes and had reorganized the eastern satrapies of the Macedonian Empire. Several semi-independent ruler grew afraid of Antigonus' power, and as a result, the Third Diadoch War broke out (314), in which Antigonus had to fight against Ptolemy, Lysimachus, and his former ally Cassander. At first, Antigonus was successful (he allied himself to his former enemy Polyperchon, and gained the Peloponnese), but he lost the east to Seleucus, an ally of Ptolemy. This was a very serious setback, and in 311, Antigonus and his rivals concluded a peace treaty. They would retain power until Alexander would become sole ruler of the entire empire when he came of age, in 305.
Although in Babylonia and Egypt, people continued to date letters according to the regnal years of the boy-king Alexander IV, the main result of the treaty was that Roxane and the twelve year old Alexander were killed: neither Cassander, nor his enemies could allow the boy to live. According to Diodorus of Sicily, the executioner was a man named Glaucias.