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Spreading of nanosized droplets was simulated on the basis of the isothermal molecular dynamics. A conclusion is made that the nanoscale droplet evolution has many common features with the macroscopic spreading. At the same time, some structure formation processes are revealed specific for the nanosized region. Observed effects include: the pyramid-like structure formation, the orientational ordering and the parquet cluster structure formation in nanodroplets composed of rod-like molecules, the replication of the structured (heterogeneous) surfaces represented by high- and low-energy segments such as striped substrates and surfaces with quadratic high- and low-energy inclusions.