They are fully convective because their relatively low temperaturature gives them a relatively high opacity to electromagnetic radiation (EMR). This favors convection over radiative transfer.
The red dwarfs have uniform composition because of the mixing of convection and eventually will convert a large fraction of their hydrogen to helium before they end their nuclear burning lives (see Wikipedia: Red dwarf: Description and characteristics)---but this has never happened to any of them yet because their main-sequence lifetimes are greater than age of the observable universe since the Big Bang 13.75(11) Gyr (see Wikipedia: Concordance model: Parameters)
The convection zone shrinks as mass increases above 1 M_☉ and disappears at ∼ 1.2 M_☉ (see Wikipedia: Radiative zone: Main-sequence stars). Stars of this mass transport energy only by radiative transfer.
Because the CNO cycle has a stronger temperature dependence than the proton-proton chain reaction, the energy input for stars > 1.3 M_☉ rises more steeply toward the center than in the stars < 1.3 M_☉, and a core convection zone occurs.
In some very massive stars, the convection zone may reach to the surface: i.e., the stellar photosphere (see Wikipedia: Convection zone: Main-sequence stars).