These can look like a puffball at first, but are called Earthstars because of the way the outer covering splits and peels back to give it a star shape. The spores are contained inside a thin-skinned puffball (fruit-body) that is exposed when the 'petals' fold back. The spores are released through a small hole at the top when rain drops hit the ball. Earthstars are found in leaf litter in the bush, and can be well camoflaged, making them difficult to find.
I have found one growing at home, in a bark garden under native trees.
Note the two developing specimens in the lower part of the photo.