Looks like Lucerna in need of some serious pruning.

Maybe the spotted one is Lucerna? And the other a form of Listada? Maybe the greenhouse effected their colors a bit more than I think they would.... the new foliage coming up on the spotted one has a purple underside... and the other one does have the distinctive light stripe down the center of the leaf... it is just a bit faint.

Your begonia is clearly rhizomatous, as I gather in checking google B. barkeri is. I'm not familiar with barkeri, which isn't surprising considering the thousands of begonia species and hybrids! Looks to be a form or hybrid of B. ricinifolia--those soft 'prickles' on the stem and forming a collar at the base of the leaf where it joins the petiole indicate that--but I don't know which one. That might help you find it though. They all take about the same care, which you seem to be providing it already--moist but never soggy potting mix, bright light but little or no direct sun, light fertilizer.

I found a way to link to my pics. it's a non knitting topic section. Here: http://www.knittingparadise.com/t-394633-1.html