It is well appreciated that the transmission of human capital from parents to children is a driver of persisting inequalities within cohorts of the population. Children of highly educated parents tend to attain higher educational achievements than children of parents of low education. Since education is a key determinant of labour market success, such inequalities in educational achievement drive inequalities in income through adulthood. Inequality arising from the educational (dis-)advantage brought about by one’s own parental education is almost universally considered “unfair” since one’s parental education is beyond one’s control, and there is broad support for corrective policy actions that may mitigate such unfair component of inequality. This is at the core of the literature on equality of opportunity. Building upon this literature, the paper first provides a fresh examination of the size of this unfairness in the contemporaneous distribution of incomes in a range of European countries (with a specific focus on the contribution of parental education along other socio-economic dimensions). It then examines how much reforms of the educational system that affected parental educational achievements (most notably extensions of compulsory schooling) mitigated or exacerbated the unfairness of the income distribution in the following generation. Exploiting multiple form of school reforms, the paper examines whether educational transmission and its impact on inequality among children comes directly (causally) from the differences in schooling (and is therefore amenable to correction by educational policy decisions) or whether it merely reflects a correlation with other transmission mechanisms that policy may not influence.