The planet would break apart, but ignoring that for a moment, it would be consumed by the star. Take the example of Jupiter hitting the earth sized white dwarf Sirius B. Jupiter's core would break up and become a thin layer around the dwarf, and it's outer layers would become a slightly less thin layer on top of that. The star would actually get a little smaller, because white dwarves size is controlled by electron degeneracy, and get smaller with more mass. Depending on the heat generated, there might be a nova as the star burns off Jupiter's hydrogen and deuterium.