Models of incipience of graphene nanotubes from carbon and boron nitri
de on diamond and cubic BN, crystals are analyzed. It is shown that th
e necessary condition for incipience of a single-layer tube is the pre
sence of a nano-size island, and formation of a multiple-layer nanotub
e requires the presence of (111) terraces on the crystallite apex. A f
ragment of a carbon tube on a diamond-like crystallite is shown to for
m a quantum ''dot'' - a quantum object with a discrete energy spectrum
. Various combinations of the C - BN nanotube - diamond-like crystalli
te structure are suggested.