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The pomegranate is a fruit-bearing deciduous shrub or small tree growing to between five and eight meters tall. The pomegranate is native to Southwest Asia and has been cultivated in the Caucasus since ancient times. It is widely cultivated throughout Afghanistan, Algeria, Armenia, Azerbaijan, Iran, Iraq, India, Pakistan, Syria, Turkey, the drier parts of southeast Asia, Peninsular Malaysia, the East Indies, and tropical Africa. Introduced into Latin America and California by Spanish settlers in 1769, pomegranate is now cultivated in parts of California and Arizona for juice production.
In the Northern Hemisphere, the fruit is typically in season from September to February. In the Southern Hemisphere, it is in season from March to May.
I beleive that the best pomegranate is produced in Iran. And the best one in Iran is produced in and around central desert opf Iran including Yazd and Kerman.