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Using non-equilibrium molecular dynamics (MD) simulations, we study heat transport in monolayer graphene sheet. We show that the thermal transport in monolayer graphene sheet exhibits a strong length dependence on thermal conductivity, reaching 2360 W/mK at 2.8 μm. By modeling a two-dimensional heat spread type of heat conduction mimicking the experimental probing using the excitation laser light focused on a graphene, the isotropic nature of heat flow in graphene is revealed, which is in support of recent experimental probing. The T-1 dependence of thermal conductivity is observed at temperatures above room temperature. A peak value at 300 K is observed with further decreasing T, in good agreement with that of carbon nanotubes reported experimentally. Thermal conductivity of graphene nanoribbons (GNRs) strongly depends on the ribbon width, which is attributed to arise from the surface phonon scattering. Furthermore, the nonlinear temperature profile is revealed for asymmetric GNRs. A fitting approach for the MD obtained temperature profile based upon the analytic solution is proposed to obtain the thermal conductivity of GNRs of asymmetric geometry. These findings shed light on tuning thermal properties of GNRs with geometry optimizations.