We have followed the adsorption and the desorption of nitrogen on the copper (100) surface in real time using scanning tunneling microscopy at elevated temperatures. This gives an unprecedented view, especially of the adsorption behavior at very low coverage. Growth proceeds by splitting of square-shaped islands of critical size without loss of C-4 symmetry. The equilibrium structures are analyzed in terms of their dimensionality and shape showing that the phase diagram comprises two periodic domain morphologies as a function of nitrogen coverage: two-dimensional (2D) array of compact nitrogen islands at low and high coverage and a quasi 1D arrangement of striped domains (rows of squares) at intermediate coverages. Furthermore, we investigated the sensitivity of the system to small changes in the elastic properties of the substrate by pre-deposition of gold on the bare copper surface. Finally, the comparison all our observations in the light of existing model predictions for long-range interactions in 2D systems reveals crucial differences and, therefore, these models have to be extended to include short range relaxation and interactions in order to reproduce the fundamental aspects of this system. (C) 2001 Elsevier Science B.V. All rights reserved.