Empirical firm size distributions are the cumulated result of underlying firm dynamics involving entry of new firms and growth, decline, and exits of incumbent firms. In this improved version of the research report "Firm size distributions" (H200306), we give an overview of firm size distributions that result as steady states from models differing in the way these firm dynamics are modelled. In the process we (i) derive common results and explain seemingly contradictory results, (ii) propose new functional forms to describe firm size distributions, (iii) give insight in the interrelationships between the distributions in terms of underlying firm dynamics, (iv) give possible firm dynamical interpretations of the parameters of the distributions, and (v) analyse to which extent the steadystate approach is able to explain the shape of firm size distributions that are encountered in practice.