The localized monolayer adsorption of noninteracting homonuclear linear k-mers on heterogeneous surfaces is analyzed by means of a theoretical approach and compared with Monte Carlo simulations. Heterogeneous surfaces are represented by two kinds of sites, the so-called bivariate surface. Deep and shallow sites with energies is an element of(S) and is an element of(D) form l x l patches distributed at random or in a chessboardlike-ordered domain on a two-dimensional square lattice. The adsorption process is analyzed following the behavior of different quantities such as coverage versus chemical potential (adsorption isotherms), mean-square fluctuation of the coverage, energy of adsorption, and differential heat of adsorption as a function of the coverage. The isotherms and the other quantities depend on the relation between the sizes of the molecule and the patch as well as on the topological distribution of the patches on the surface.