  We present a comparative study of high carrier density transport in mono-,
bi-, and trilayer graphene using electric-double-layer transistors to
continuously tune the carrier density up to values exceeding 10^{14} cm^{-2}.
Whereas in monolayer the conductivity saturates, in bi- and trilayer flling of
the higher energy bands is observed to cause a non-monotonic behavior of the
conductivity, and a large increase in the quantum capacitance. These systematic
trends not only show how the intrinsic high-density transport properties of
graphene can be accessed by field-effect, but also demonstrate the robustness
of ion-gated graphene, which is crucial for possible future applications.
