The structure of the dye layer adsorbed on the titania substrate in a dye-sensitized solar cell is of fundamental importance for the function of the cell, since it strongly influences the injection of photoelectrons from the excited dye molecules into the titania substrate. The adsorption isotherms of the N719 ruthenium-based dye were determined both with a direct method using the depth profiling technique neutral impact collision ion scattering spectroscopy (NICISS) and with the standard indirect solution depletion method. It is found that the dye layer adsorbed on the titania surface is laterally inhomogeneous in thickness and there is a growth mechanism already from low coverage levels involving a combination of monolayers and multilayers. It is also found that the amount of N719 adsorbed on the substrate depends on the titania structure. The present results show that dye molecules in dye-sensitized solar cells are not necessarily, as presumed, adsorbed as a self-assembled monolayer on the substrate.