We quantify intergenerational and assortative processes by comparing different degrees of kinship within the same generation. This “horizontal” approach yields more, and more distant kinship moments than traditional methods, which allows us to account for the transmission of latent advantages in a detailed intergenerational model. Using Swedish registers, we find strong persistence in the latent determinants of status, and a striking degree of sorting – to explain the similarity of distant kins, assortative matching must be much stronger than previously thought. Latent genetic influences explain little of the variance in educational attainment, and sorting occurs primarily in non-genetic factors.