Common name: Elephant Bush
Family: Portulacaceae
Genus: Portulacaria
Species afra
Plant Link: http://plantsdatabase.com/go/350/
I have one exactly like this one. I was also looking for its name and now I have found it here. Mine is about ten years old. Slow grower. Does not ask for much attention - survives well and does well too!
The leaves of mine are not as broad as yours. Has somewhat darker green shade. I water mine once or twice a week. It is the one in the picture around the centre almost touching the trellis in this http://davesgarden.com/fp.php?pid=10978. I think you can make it out from this long-shot how small the leaves are.
this is a nice looking bonsai!!
Thank you, tiG.
Dinu, the leaves on mine are larger and of a lighter shade because it gets very little sun.
I love these, will have to try to locate one!