What kind of metamorphism occurs when hot magma comes near or in contact with existing rock?
Metamorphic rocks are one of the three basic types of rock (the other two are igneous and sedimentary). Metamorphic rocks are formed from other types of rock through applied heat or pressure. In other words, the rock when exposed to heat or pressure undergoes a chemical transformation that changes its mineral composition into something entirely new, thus forming a new type of rock. The act of the rock changing into metamorphic rock is called metamorphism.
Within metamorphic rocks, there are two basic categories of metamorphism: contact and regional. Regional metamorphism occurs over a wide range of area from either general heat near the core of the Earth or pressure from overlying rocks. Contact metamorphism results from the direct contact of rock with a source of magma. The intense heat from the magma is enough to alter the surrounding rock. So the answer to your question is contact metamorphism.