Glass films created by vapor-depositing molecules onto a substrate can exhibit properties similar to those of ordinary glasses aged for thousands of years. It is believed that enhanced surface mobility is the mechanism that allows vapor deposition to create such exceptional glasses, but it is unclear how this effect is related to the final state of the film. Here we use molecular dynamics simulations to model vapor deposition and an efficient Monte Carlo algorithm to determine the deposition rate needed to create ultra-stable glassy films. We obtain a scaling relation that quantitatively captures the efficiency gain of vapor deposition over bulk annealing, and demonstrates that surface relaxation plays the same role in the formation of vapor-deposited glasses as bulk relaxation does in ordinary glass formation.Compared to their liquid-cooled counterparts, vapordeposited glasses often have a higher density [1], a higher kinetic stability [2][3][4], and a lower heat capacity [5]. This makes them promising materials for a wide range of applications, such as drug delivery [6], protective coatings [7,8], and lithography [9]. Identifying the microscopic process that gives rise to these properties is thus crucial to designing novel amorphous materials [10]. Vapor deposition indeed does not systematically result in glasses with improved characteristics. It is observed that the substrate ought to be held at a specific temperature (around 85% of the glass transition temperature T g of the liquid [3]) and that the deposition rate must be sufficiently slow [11] to get optimal films. A microscopic explanation for the optimality of 0.85T g , and an estimate of what is a "sufficiently slow" deposition rate are, however, still lacking. Moreover, while simulations and experiments have shown that vapor-deposited glasses may lie lower in the potential energy landscape than liquidcooled glasses [3,[11][12][13][14][15][16], and sometimes have the same structure as glasses of a comparable energy [14], it is not known whether vapor deposition can provide truly equilibrium configurations, especially below T g .Here we provide a quantitative test of the role of surface mobility in the creation of vapor deposited glasses. More specifically, we answer two key questions. (i) How much more efficient is vapor deposition than standard cooling in creating a glass or, more precisely, given a substrate temperature and a deposition rate, what is the effective cooling rate that would produce similar configurations? (ii) What is the deposition rate needed to produce fully equilibrated configurations? Answering these questions is a challenging program that requires characterizing equilibrated films at temperatures sufficiently low for a large difference between surface and bulk relaxation to have developed, as well as measuring bulk and surface dynamics in a same material, over the same temperature range, and under the same thermodynamic conditions. We overcome these problems by using, on a properly chosen polydisperse Lennard-Jones model, a swap Mo...