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Is being unarmed, you know, going fisticuffs, governed by two handed or does it just not have a skill of its own?

It's not governed by any skills. It does not have any perks. Punching enemies does not count towards any skill's increasement (except possibly Sneak if you punch while sneaking?).

there is a perk in the heavy armor tree which adds your heavy gauntlets armor rating to the damage done by unarmed strikes + there are the gauntlets of the pugilist which increases the damage from unarmed strikes. so having the perk and enchanting a deadric gauntlet with a high amount of pugulist enchantment, you can do a lot of damage.

Ok thanks guys. Ima have to go get me a pair of those gloves then.

Argonanza wrote:(except possibly Sneak if you punch while sneaking?).

Yep.
You should read over this before you get too invested.
It works fine, but some of the wording is a bit misleading.
And you can put that Unarmed damage enchantment on a ring, too.