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only Hitsugaya and Yoruichi can be called random. Else in the list was pretty much explained in the manga. Ichigo learned in 3 days with the help of Kisuke (smartest in the verse) who himself learned in 3 days. Vasto Lorde was his form in which his inner hollow White gained full control over his body. FGT was his Clan (shiba) technique which he learned with the help of his father in months.