We present a dynamic Monte-Carlo model involving lateral interactions and different adsorption sites ͑top, fcc and hcp͒. 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 Rh͑111͒ during adsorption and the temperature programmed desorption ͑TPD͒ of NO from Rh͑111͒ under UHV conditions. The formation of c͑4ϫ2͒-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 ͑2ϫ2͒-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 NϩO 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. NϩO on the other hand form islands with a lower coverage ͑0.30-0.35 ML͒ due to the considerable next-next-nearest-neighbor repulsion. Top bound NO ͑above 0.50 ML initial coverage͒ does not dissociate during TPD. It desorbs in a separate peak at 380 K.