Using a computer simulation, we have studied the random sequential adsorption of stiff linear k-mers onto a square lattice. Each such particle occupies k adjacent lattice sites. During deposition, the two mutually perpendicular orientations of the particles are equiprobable, hence, a macroscopically isotropic monolayer is formed. However, this monolayer is locally anisotropic, since the deposited particles tend to form domains of particles with the same orientation. Using the “excluded area” concept, we have classified lattice sites into several types and examined how the fraction of each type of lattice site varies as the number of deposited particles increases. The behaviors of these quantities have allowed us to identify the following stages of domain formation: (i) the emergence of domain seeds, (ii) the filling of domains, and (iii) densification of the domains.