I love the full size of my areolas. Can that be preserved? Most of the breast lifts I see have small areolas. (photos)

It is possible to preserve the size of your areolae with a breast lift. Just make your wishes known to your surgeon. However, you should know that your areolae may be reshaped just to maintain a proportionate result. 

Far more important than the technique is the skill and experience of your plastic surgeon. Choose your surgeon rather than the technique and let them explain why one technique may be better than another. See the below link on some suggestions on finding the most qualified Plastic Surgeon for a mastopexy

It is possible to request larger areolas although there are some limitations technically and also the way you heal often dictates the final result. Also the technique can vary the diameter. Discuss your wishes with your PS