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Muqali served Genghis' enemy (serving as a slave or Nak for Genghis' rival, the aunt of his father of the Jurchen clan) in his early days but was captured. Genghis rewarded the defiant Mukhali for his integrity and wisdom, and afterwards was a loyal companion.
During the coronation of Genghis Khan, Muqali was given the command of the Third Tumen and control over the Eastern mingghans. In 1211, he participated in the Battle of the Badger Mouth, the decisive battle in the first stage of the Mongol–Jin War.
After Genghis Khan decided to go to war with the Khwarezmid Empire, he gave control of all Turco-Mongol forces to Muqali and gave him the title of King, a largely ceremonial title. Despite Genghis Khan having most of the main Turco-Mongol forces taken away and sent to the West, Muqali was able to subdue most of Northern China with his small force of around 20,000 men, although some historians give figures of between 40,000 and 70,000 men.
In 1217 Muqali attacked the province of Hebei as well as northern Shandong and northern Shaanxi. This was an important agricultural area, which Muqali had largely subdued by 1219. In 1220 Muqali turned his attention to the rest of Shandong; four towns were captured, but the hard-pressed Jin managed to hold on elsewhere in the province.
Muqali's last campaign began in 1222. He crossed the Wei River and attacked south, capturing towns that had already been plundered by a previous Mongol general-Samuqa, who suddenly disappeared from Mongol history. Meanwhile, the Jin launched a counter-attack into the province of Shansi. Muqali swiftly raced to the area; the Jin fled without giving battle. Besieging another town, Muqali became seriously ill and died shortly thereafter in 1223. On his deathbed, Muqali declared with pride that he had never been defeated.
After his death, Genghis Khan gave command to Muqali's son Birdlu. In seven years of campaigning in northern China, he had reduced the Jin empire to the province of Henan. He had proven himself to be an excellent general who was indefatigable in his efforts to serve his master, Genghis Khan.
After his death, descendants of Mukhali served the Great Khan of the Mongols, especially those of the Toluid lineage. A few of his descendants, such as Antong and Baiju, later became prominent officials in the Confucian fashion of the Yuan Dynasty founded by Kublai Khan in China.
Retainers of the Toluid Hulagu participated in the conquest of Persia, then called Mollai, and later founded the Jalayirid Dynasty which ruled from Baghdad after the collapse of the Hulaguid Ilkhanate.
For more information on Muqali's Northern China campaign and much else, see 
UPDATE SEPTEMBER 2015: The greatest book on Muqali and the Mongols of that time is clearly 
- "Genghis Khan Conqueror of the World", Leo de Hartog.
- "Genghis Khan his conquests, his empire, his legacy", Frank McLynn