If you find yourself with one of these, leave them on the momma plant to create a real conversation piece. These plants are long-lived and the larger they get the more bloom spikes they will send up. If you find any dead or broken roots, snip them off. Sometimes Phals will kiky from the bloom spike or base. These plants can be potted separately or keep on the momma plant.
Dendrobiums keep sending up new shoots from the base.
Some vigorous plants will produce many new shoots from all sides. When the pot is full to over-flowing, you can divide the plant, keeping at least one or two good shoots per new plant, or just move the whole thing into a larger pot. With Dendrobiums, you will want to remove old dead canes to keep the plant attractive. Orchid potting medium is sold in better garden centers. A product called Servo is wonderful for potting most types of orchids.