High-field electron transport properties in a two-dimensional nanolayer are studied by an application of the anisotropic nonequilibrium distribution function, a natural extension of the Fermi-Dirac distribution by inclusion of energy gained/absorbed in a mean free path (mfp). The drift velocity for conical band structure of graphene is shown to rise linearly with the electric field in a low electric field that is below the critical electric field. The critical electric field, equal to thermal voltage divided by the mfp, marks the transition from ohmic linear transport to saturated behavior in a high electric field. As field rises beyond its critical value, the drift velocity is sublinear resulting in ultimate saturation; the ultimate saturation velocity is comparable to the Fermi velocity in graphene. The quantum emission is found not to affect the mobility, but is efficient in lowering the saturation velocity. Excellent agreement is obtained with the experimental data for graphene on silicon dioxide substrate.

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