Experimental studies have reported several types of Si monolayer structures that are formed on metal surfaces. These structures typically show the topology of a honeycomb bonding network, but differ in terms of corrugation and surface coverage. Using first-principles calculations, we identify atomic-scale mechanisms that underlie the appearance of different configurations as coverage increases during Si deposition on silver. The key point is that any extra Si adatoms that land on preformed silicene films can be incorporated in the honeycomb network and form bonds with underlying Ag atoms. As a result, the corrugation profile changes, giving rise to varying overlayer geometries. We also show that the same set of mechanisms control the appearance of silicene films on an iridium substrate. The results address available experimental data, but also probe the stability and properties of silicene wetting films that have not been observed yet. (C) 2013 Elsevier B. V. All rights reserved.