In which form of reproduction does The offspring grow specifically for the stem or root of a plant

The phenomenon you are referring to is known as vegetative reproduction. In this type of reproduction, the offspring are produced from a part of a plant other than the seed, and they inherit all the genetic characteristics of the parent plant. In some plants, such as potatoes, the stem or root of the parent plant is used to produce the offspring through a process called vegetative propagation. The new plants that grow from these parts are identical to the parent plant and can be used for cultivation.