A lattice model for polydisperse rectangles on a square lattice has been used to study the behavior of rodlike surfactant aggregates at the solid-liquid interface. In principle it is possible to obtain the three parameters of the model from 2D MFL (mean field lattice) calculations. The aggregates grow with increasing chemical potential. If the caps become more unfavorable, the average length of the rod increases. If the average length exceeds a certain value, a second-order transition from an isotropic to a nematic phase takes place. The growth of the aggregates is promoted by the nematic ordering. a nearly exact relation between the number of aggregates at the surface at the isotropic-nematic transition line, and the average aspect ratio has been found by a fit of the numerical data. If the number of aggregates decrease, the average aspect ratio to obtain nematic ordering has to increase.