Is the 529 limit of $10,000 (for married filing joint) per household or per child account?

TurboTax is telling me that I cannot enter more than $10,000 on Part 1 line 1 of the 529 section.  But I have friends that say the $10,000 limit is per child.  (Although they are in NJ and I am in NY).  Could someone confirm if the limit is per household or per child?  And is there a difference between NY and NJ?