We consider the dynamics of squeeze-out of a molecularly thin confined two-dimensional (2D) liquidlike layer. The squeeze-out is described by a generalized 2D Navier-Stokes equation which is solved exactly for the limiting case where the squeeze-out nucleates at the center of the contact area, and where the (perpendicular) three-dimensional pressure profile is Hertzian. We also present numerical results for the case where the nucleation is off-center. The theoretical results are in good agreement with recent experimental data by two of us for octamethylcyclotetrasiloxane. In light of our theoretical model calculations, we also discuss the spatially resolved diffusion experiments of Mukhopadhyay [Phys. Rev. Lett. 89, 136103 (2002)]. Here, we obtain a puzzling disagreement between theory and experiment which requires more investigation. (C) 2003 American Institute of Physics.