Tapping mode Atomic Force Microscopy has been used to investigate the spreading of molecularly thin (up to a few nanometers) precursor films emerging from drops of ionic liquids that partially wet smooth mica surfaces. The lateral extent of the film increases with time and reaches values as large as few millimeters within 12 hours. From the observations of the precursor film at several positions and times, its extent ℓ(t) was estimated and used to determine bounds for the coefficient D1 (defined by ℓ(t) = √D1t) that characterizes the rate of spreading. The spreading rate and the film morphology (at micrometer scale) for three different ionic liquids of varying cation molecular structure are compared.