  We use a van-der-Waals pickup technique to fabricate different
heterostructures containing WSe$_2$(WS$_2$) and graphene. The heterostructures
were structured by plasma etching, contacted by one-dimensional edge contacts
and a topgate was deposited. For graphene/WSe$_2$/SiO$_2$ samples we observe
mobilities of $\sim$12 000 cm$^2$/Vs. Magnetic field dependent resistance
measurements on these samples show a peak in the conductivity at low magnetic
field. This dip is attributed to the weak antilocalization (WAL) effect,
stemming from spin-orbit coupling. Samples where graphene is encapsulated
between WSe$_2$(WS$_2$) and hBN show a much higher mobility of up to $\sim$120
000 cm$^2$/Vs. However, in these samples no WAL peak can be observed. We
attribute this to a transition from the diffusive to the quasiballistic regime.
At low magnetic field a resistance peak appears, which we ascribe to a size
effect, due to boundary scattering. Shubnikov-de Haas oscillations in fully
encapsulated samples show all integer filling factors, due to complete lifting
of the spin and valley degeneracy.
