The late stage kinetics of the spreading of a smectic nanodrop on a solid surface was investigated by direct and real time imaging of a three molecular layer patch using the SEEC microscopy. Experimental data do not conform to the only available theory, which covers only weakly stratified liquids. A new model is proposed, in remarkable agreement with experiments, in which the spreading mechanism appears to be a quasi-static process ruled by solid/liquid interactions, 2D Laplace pressure, and separate edge and surface permeation coefficients.