For nursing mothers and growing kits (up to about five to six months) around here they're pretty much fed as much as they want.
The bunnies here are angoras, so they're fed high protein bunny pellets as the base feed with rolled barley & BOSS added in. They also get lots of various forages. Around here it's tall grasses (Guinea, cane, elephant, Reznor, etc.) as well as mulberry leaves and twigs, ti leaves, assorted herbs, dandelions, plantain, etc., etc. We don't feed hay because it's too expensive (almost $40 a small bale) and it mildews too quickly.
I've noticed that if they are fed a variety of things as babies, they're much more receptive to new foods as adults. If they've only had a very limited diet ad youngsters, they sometimes won't expand their diet to other things as adults.