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I believe that Hinata and Naruto would have three children. In my opinion, there would be two girls and one boy. The oldest would be a girl possibly named Nina. She'd have hair a little longer than shoulder length, it would be black with blonde streaks, and she'd keep it in two pigtails until she went to bed. Nina would also have one pale lavender eye (like Hinata's) and the other eye would be bright blue (like her fathers). She would be loud, a prankster, but very sincere and caring.

Then there would be a boy who might be name Hiro. Hiro's hair would probably resemble his fathers. He'd have black hair and bright blue eyes and would be shy and quiet. Although, he'd always protect the ones he cares about and won't let anybody push around his sisters or himself.

Last, would be a girl name Nara. She'd have short, blonde hair and pale lavender eyes. She'd be very outpoken but, extremly shy around the guy she likes. Nara would never let down others and in the beginning she wouldn't be the best ninja (just how her father started out).

Well, those are Naruto and Hinata's children in my opinion. I don't believe they'd inherit the Kyuubi's chakra but, I believe they would be able to use the Byakugan. Since, that does seem like a dominant trait.