I would think they have to do with your breasts size. If you have an A cup you're gonna have something proportioned to that. Whether you're black, white or whatever they will be different because within each race there are different breast sizes.
i think it depends on size and how fast your breasts grow ans stretch. if they grow and stretch really fast than you will have larger areolas. if they grow slowers/stretch slower than they will be smaller. I know women with A cups with large areolas and D cups with small ones
the larger the breast size, the larger the areolas. the areolas evolved to be big enough to be visible to a baby's eyes because when babies are born they can't see properly their eyes are not fully developed, some say babies can see only black and white first few weeks after birth, so in order to drink milk the areolas were evolved to be visible to the baby and trigger the breastfeeding reflex
It's not race related at all, but is related to breast size. I'm a DD with dollar-sized areolas, but when I was younger and my breasts were smaller the areolas were smaller and more proportionate to the breast size.
This is a confusing post, you said white girls don't have large areola then in the second sentence you mention "It seems that the women I've seen with larger areolas were Italian, Latina" which stragely enough Italian girls are white and latina girls can be white.
Ignoring that there is no correlation between race and areola size, just like everything else as simple of an answer as this is, it varies depending on the individual.