No body can be pure after generations living abroad. Me too, I'm not pure ethnic Chinese either. 心所安处,即是吾乡。
Rules for determining if you are Chinese:
1. If you are born as a Chinese citizen, you are Chinese.
2. If both of your parents are Chinese, you are Chinese.
3. If only one of your parents is Chinese, but you were raised to believe yourself to be Chinese, then you are Chinese.
Rules are applied in order.
For example:
1. I'm born a Chinese citizen, so I am Chinese according to rule #1
2. My wife was also born a Chinese citizen, so my kids are Chinese according to rule #2
3. If my son marries another Chinese person, their kids are also Chinese.
4. If my son marries a non-Chinese person, but raises their kids to believe themselves as Chinese, then my grandkids are also Chinese.
5. If my grandkids are Chinese, regardless of the nationality of their other parent, then their kids are determined to be Chinese or not based on rules #2 and #3.
6. If my grandkids, for some reason, are not Chinese, and they marry someone who is not Chinese either, then their kids are not Chinese. In order for my great-grandkids get back into the Chinese identity, they'd have to marry a Chinese person and raise their kids as Chinese, which would make their kids Chinese (but still not them).
Those are the rules I came up with, feel free to pick them apart!