Evaporation of water nanodroplets on a hydrophilically adjusted graphene sheet was studied based on a molecular dynamics approach. Suspended graphene was used as a physically heterogeneous surface, and fixed graphene was considered as an ideally flat surface. State of the triple-phase contact line (TPCL) and shape evolution were addressed at four different temperatures on both substrates. Additionally, contact angle (CA) was studied during 3 and 22.5 ns simulations in both closed and opened conditions. The observed constant contact angle regime was predictable for the fixed graphene. However, it was not expected for the suspended system and was attributed to the oscillations of the substrate atoms. The size of the nanodroplet also affects the constant-contact-angle mode in both systems, when the number of water molecules decreases to less than 500. The oscillations created a surface on which physical heterogeneities were varying through time. Examination of the evaporation and condensation processes revealed higher rates for the fixed systems. Local mass fluxes were calculated to reveal the contribution of TPCL and meridian surface (MS) of the nanodroplet to evaporation and condensation. The obtained results indicate similar values for the mass flux ratio at the TPCL, which remains twice as large as the MS for both suspended and fixed graphene. The results confirm the assumption that a surface with varying heterogeneities can overwhelm the droplet and act as an ideally flat surface.