We have performed extensive simulations of random sequential adsorption and diffusion of k-mers, up to k = 5 in two dimensions with particular attention to the case k = 2. We focus on the behavior of the coverage and of vacancy dynamics as a function of time. We observe that for k = 2,3 a complete coverage of the lattice is never reached, because of the existence of frozen configurations that prevent isolated vacancies in the lattice to join. From this result we argue that complete coverage is never attained for any value of k. The long time behavior of the coverage is not mean field and nonanalytic, with t(-1/2) as leading term. Long time coverage regimes are independent of the initial conditions while strongly depend on the diffusion probability and deposition rate and, in particular, different values of these parameters lead to different final values of the coverage. The geometrical complexity of these systems is also highlighted through an investigation of the vacancy population dynamics.