I have never heard of caulerpa with white on it - I know there are different kinds, but I'm only familiar with what I have (grape caulerpa). Does it look like this? I like it and so far it hasn't taken over, but I definately can see how it could happen. For now, I just trim it back occasionally, although, it isn't a steady grower. Sometimes it grows in spurts and I have to trim back the new shoots. Otherwise I really enjoy it.