The megalonychid ground sloths first appeared in the early Oligocene, about 35 million years ago, in southern Argentina (Patagonia). Megalonychids first reached North America by island-hopping, perhaps from the Antilles. With the rise of the land bridge at Panama there were further northward migrations as part of the Great American Interchange. Some lineages of megalonychids increased in size as time progressed. The first species of these were small and may have been partly tree-dwelling, whereas the Pliocene (about 5 to 2 million years ago) species were already approximately half the size of the huge Late Pleistocene Megalonyx jeffersonii from the last ice age. Some West Indian island species were as small as a large cat; their dwarf condition typified both tropical adaptation and their restricted island environment. This small size also enabled them a degree of aboreality.
Read more: http://en.wikipedia.org/wiki/Megalonychidae