So far I think it's a mimosa but it hasn't bloomed. I understand that's expected since the tree popped up only last summer. So now the bottom branches are falling off. Is that normal for this time of year? If so, does anyone know how far up the branches will off? If they all do then it's going to look very odd in the winter. Simply a "Y" of a tree. So far about half have fallen off.

It could be Selaginella martensii. It could be one of the many cultivars of Selaginella kraussiana. Joe

I'd agree, ot doesn't quite have that fern look to it. Do you have photos of the under side of the leaves? Also where the stems arise from the ground. New leaves in ferns unfurl, giving them the name "crozier", after a bishop's staff.

There is a fern called Nephrolepsis exalta "fluffy ruffles" which fits your description but I don't think has any sort of perfume. There is another fern called Paesia scaberula which has a sweet spicy perfume but I don't think the fronds are long enough to be the one you have. Perhaps you could Google some images to see if either one fits. Cheers, Dee.