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We perform molecular dynamic simulations of liquid nanoparticles deposited ona disordered substrate. The motion of the nanoparticle is characterised by a'stick and roll' diffusive process. Long simulation times ($\simeq \mu s$),analysis of mean square displacements and stacking time distribution functionsdemonstrate that the nanoparticle undergoes a normal diffusion in spite of longsticking times. We propose a phenomenological model for the size andtemperature dependence of the diffusion coefficient in which the activationenergy scales as $N^{1/3}$.Comment: Accepted for publication in Phys. Rev.

Diffusion of a liquid nanoparticle on a disordered substrate