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Consider the classical (2+ 1)-dimensional Solid-On-Solid model above a hard wall on an L× L box of Z2. The model describes a crystal surface by assigning a nonnegative integer height ηx to each site x in the box and 0 heights to its boundary. The probability of a surface configuration η is proportional to exp (− βH (η)), where β is the inverse-temperature and H (η) sums the absolute values of height differences between neighboring sites. We give a full description of the shape of the SOS surface for low enough temperatures. First we show that with high probability (whp) the height of almost all sites is concentrated on two levels, H (L)=⌊(1/4β) log L⌋ and H (L)− 1. Moreover, for most values of L the height is concentrated on the single value H (L). Next, we study the ensemble of level lines corresponding to the heights (H (L), H (L)− 1,...). We prove that whp there is a unique macroscopic level line for each height …