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High-throughput single-cell methods have uncovered substantial heterogeneity in the pool of hematopoietic stem and progenitor cells (HSPCs), but how much instruction is inherited by offspring from their heterogeneous ancestors remains unanswered. Using a method that enables simultaneous determination of common ancestor, division number, and differentiation status of a large collection of single cells, our data revealed that murine cells that derived from a common ancestor had significant similarities in their division progression and differentiation outcomes. Although each family diversifies, the overall collection of cell types observed is composed of homogeneous families. Heterogeneity between families could be explained, in part, by differences in ancestral expression of cell surface markers. Our analyses demonstrate that fate decisions of cells are largely inherited from ancestor cells, indicating the importance of common ancestor effects. These results may have ramifications for bone marrow transplantation and leukemia, where substantial heterogeneity in HSPC behavior is observed.