My PTP is 14 years old and up until 3 years ago had a single 'tail' at the top which started to rot and die off. I decided to leave it alone. When the top returned to health we named it Cousin It. Now it has about 8 large 'babies at its base that are strong and lush. At Christmastime I put a santa hat on 'It' and two large comical eyes.

Nevermind, I found the info I needed

Hi, Andrew - Please tell us more about your watering habits. If you have been keeping the soil continually moist or have been watering when the top inch or two of the soil gets dry, it's likely you've "watered it to death" and the pathogen is any one of the several damping-off family of fungi. Too much water and not enough air in the root zone sets the stage for a weakened plant (in terms of its natural defenses, which are directly related to the plant's metabolic rate) and fungal infections. Ponytail palm is such a durable plant, it's often erroneously suggested they thrive on neglect. They thrive on the type of care that ensures cultural conditions are in the sweet spot and not near or beyond the limits they're programmed (genetically) to tolerate. While they might survive long periods of neglect that leads to the soil becoming completely dry, they don't appreciate that type of treatment. Still, if you had to choose between trying to keep the soil continually moist or allowing the soil to go completely dry before the next watering, you should favor the later. They can "tolerate" being too dry, but cannot tolerate being too wet. Also, it's a plant that appreciates all the sun you can give it, but don't think that its present low light location is a part of your plant's demise. Al

That's an interesting question - I'd answer with 'both'. They're as you've noted branches, and they're young enough (and not woody) to detach and grow them as pups and into separate plants, I'd guess. I've never done it but I think it can be done.