Second photo, of the java fern, shows new java fern plants growing from the tip of the parent leaf. Not uncommon at all-though in my experience it happens most when the plant is stressed, which transplanting certainly counts as.
You can trim the leaf if you don't like how they look, or let them grow as they are. Eventually they'll come lose on their own or you can remove them to discard or propogate elsewhere as you choose.
Last edited by Knotyoureality; 03-10-2013 at 04:06 AM.