Maybe you are with lucky with your "restarting cellphone", i am from brazil, here we have a lot of poor cellphones doing this!
The solution for this problem is generally simple!
When this starts, cellphone restart only with sim inserted like crazy.
I will use for this example the cellphone lg e615f, that do this when gets older! very common in brazil!
1 -It uses a battery called BL-44JN with 1540Mah. This is the original battery from the manufacturer,, when the cellphone get older, it looks like everything ok, but it starts to reboot, only when sim is inserted, but without sim it stop restarting.
2- If you send it to a technican here(like me ;-), he will just change the ORIGINAL battery BL-44JN(1500mah) to the BL-44JH (1700mah), and for some crazy reason it solves the problem, and it will works very fine, for long years ;-) yes i am the technican and i dont know why this works, but work every time!
So what i recommend for nexus 10? Just change the battery for one of the same specification first, even if it looks fine, if the problem persists, try a generic "bigger Mah value" battery (but with the same size, and polarity, you can found some china generic with a longer duration i think on the internet)
I know its sounds Strange, but it really solved problem with a lot of cellphones of friends =]
And f your cellphone is broken, it can get worst, i think so you can try! but if it explodes, just cook some hamburger with the cellphone fire... (sorry if i have a bad english)