In this paper, we characterize the relationship between the initial distribution of human capital and physical inheritances among individuals and the long-run distribution of these two variables. In a model with indivisible investment in education, we analyze how the initial distribution of income determines the posterior inter-generational mobility in human capital and the evolution of intra-generational income inequality. This analysis enables us in turn to characterize the effects of fiscal policy on future income distribution and mobility when the composition of inter-generational transfers is endogenous. We find that a tax on inheritance results in both less inter-generational mobility and smaller investment in human capital. However, a tax on labor income may promote human capital accumulation if the education premium is sufficiently high.