We present a dynamic Monte-Carlo model involving lateral interactions and different adsorption sites (top, fcc and hcp). Using this model in combination with kinetic parameters from UHV experiments and lateral interactions derived from DFT calculations we have reproduced the ordering behavior of NO on Rh(111) during adsorption and the temperature programmed desorption (TPD) of NO from Rh(111) under UHV conditions. The formation of c(4x2)-2NO domains at 0.50 ML coverage is shown to depend strongly on the next-next-nearest-neighbor repulsion between the NO adsorbates in our model. The formation of the (2x2)-3NO structure at higher coverage follows from the avoidance of the strong next-nearest-neighbor repulsion in favor of the occupation of the top sites. A single-site model was able to reproduce the experimental TPD, but the lateral interactions were at odds with the values of the DFT calculations. A three-site model resolved this problem. It was found that all NO dissociates during TPD for initial coverages of NO below 0.20 ML. The nitrogen atoms recombine at higher temperatures. For NO coverages larger than 0.20 ML, 0.20 ML NO dissociates while the rest desorbs. This is due to a lack of accessible sites on the surface, i.e., sites where a molecule can bind without experiencing large repulsions with neighboring adsorbates. For NO coverages above 0.20 ML, the dissociation of NO causes a segregation into separate NO and N+O islands. The dissociation causes the surface to be filled with adsorbates, and the adsorbates are therefore pushed closer together. NO on one hand can easily be compressed into islands of 0.50 ML coverage, because there is no large next-next-nearest-neighbor repulsion. N+O on the other hand form islands with a lower coverage (0.30-0.35 ML) due to the considerable next-next-nearest-neighbor repulsion. Top bound NO (above 0.50 ML initial coverage) does not dissociate during TPD. It desorbs in a separate peak at 380 K. (C) 2003 American Institute of Physics.