About a year and a half ago, I took a few "babies" off of a friends plant and since then, they have fourished, becoming several full grown plants. They are really neat, with "babies" around the perimeter of each leaf. These "babies" will randomly fall from the leaves onto the soil and begin growing into their own full sized plants. Recently (within the past few weeks), I've noticed that a few of the "babies"--still attached to leaves-- have begun growing "babies" of their own (3 generations, all attached to each other). I have asked several people (supposedly knowledgable about plants) and consulted several books and websites and have been unsuccessful in identifying this plant. If anyone could help, I would be grateful. I have attached a few pictures, but have many more if other views are needed to ID it. Thanks so much.