Diane,
Looks most likely to be Nerines of some description. The bulbs are not the right shape for freshly shot Calostemma (the Aus native that Lesley was trying to think of) which are much more elongated in appearance. They could also be some form of Haemanthus, as they are another than germinates without any outside influence. Most of the Haemanthus I have come across have fatter bulbs (well, shorter and broader dimensions anyway) form than those in your pics, but it could just be a different species to those I am used to. I'd be leaning towards Nerine myself.