We exploit the bilateral and skill dimensions from recent data sets of international migration to test for the existence of Zipf's and Gibrat's Laws in the context of aggregate and high-skilled international immigration and emigration using graphical, parametric and non-parametric analysis. The top tails of the distributions of aggregate and high-skilled immigrants and emigrants adhere to a Pareto distribution with an exponent of unity i.e. Zipf's Law holds. We find some evidence in favour of Gibrat's Law holding for immigration stocks, i.e. that the growth in stocks is independent of their initial values and stronger evidence that immigration densities are diverging over time. Conversely, emigrant stocks are converging in the sense that countries with smaller emigrant stocks are growing faster than their larger sovereign counterparts. Lastly, high skilled immigration and emigration stocks expressed in levels or as densities all exhibit signs of convergence. We conclude by discussing some competing mechanisms that could be driving the observed patterns including: differing fertility rates, reductions in emigration restrictions, migrant sorting and selective immigration policies, immigrant networks and persisting wage differentials.