Although the unexpectedly fast capillary flow of water (partial wetting) in graphene nanoslits has been reported, the wicking dynamics of total wetting liquid in a nanocapillary have not been studied. In this work, the spreading behavior on graphene sheets and the imbibition process in graphene nanochannels are explored by molecular dynamics for ethanol (total wetting). For spreading dynamics, two regimes are identified: inertia-dominated initial spreading and viscous spreading with an exponent greater than Tanner's law. For imbibition dynamics, the total wetting liquid behaves quite differently from the partial wetting liquid. The advancing motions of both the precursor film and main flow are clearly seen, and their advancing lengths are proportional to the square root of time. However, the proportional constant of the former, which is independent of channel widths, is greater than that of the latter, which decreases with increasing channel widths. Both the thickness of the precursor film and the diameter of curvature of the menisci, which is less than the channel width, grow with increasing channel widths. For very narrow nanoslits, the precursor film cannot be distinguished from the main flow, and the surprisingly rapid imbibition behavior is observed.