Grafting
Joining a shoot or bud of one plant onto the roots of another so they grow as one.
Also: budding
In grafting, the top of one plant, called the scion, is joined to the rooted base of another, called the rootstock. The cut surfaces are bound together until they knit. The rootstock supplies vigour, hardiness or disease resistance, and the scion supplies the flowers. Most garden roses are made by budding, a form of grafting that uses a single bud. Shoots that sprout from below the join belong to the rootstock and should be removed.