The Science Behind Grafting
Branches and leaves obtain water via tube like vessels (xylem) that run from roots up to the shoot tips. Sugar produced by the leaves moves down a different type of vessel (phloem) to the roots. For grafts between two plants to be successful in the long-term, new connections must be generated between these conducting vessels.
The stems of woody plants have a single ring of cells, called the cambium, which have the potential to produce both water and sugar conducting vessels. Soon after plants are grafted, the cut surfaces begin to heal by generating generalized cells that lock the parts together. Then, if the cambiums of both stems are aligned, they will generate new vessels that connect the grafted pieces so that water and sugar are now able to move through the graft union.
As with human organ transplants, rejection can occur if the two partners are too unrelated. In plants, where a classical immune system is not present, compatibility is more likely. Success is correlated to how closely the plants are related. No permanent grafts have ever been produced between plants that are in different families.
In nature, root to root or stem to stem grafting can occur spontaneously when adjacent roots or stems grow in girth pressing against each other.