As vertebrate embryos develop to adulthood, their organs undergo marked changes in size and tissue architecture. The heart acquires muscle mass and matures structurally to fulfil increasing circulatory needs, a process that is incompletely understood. Here we used multicolour clonal analysis to define the contributions of individual cardiomyocytes as the zebrafish heart undergoes morphogenesis from a primitive embryonic structure into its complex adult form. We find that the single-cardiomyocyte-thick wall of the juvenile ventricle forms by lateral expansion of several dozen cardiomyocytes into muscle patches of variable sizes and shapes. As juvenile zebrafish mature into adults, this structure becomes fully enveloped by a new lineage of cortical muscle. Adult cortical muscle originates from a small number of cardiomyocytes--an average of approximately eight per animal--that display clonal dominance reminiscent of stem cell populations. Cortical cardiomyocytes initially emerge from internal myofibres that in rare events breach the juvenile ventricular wall, and then expand over the surface. Our results illuminate the dynamic proliferative behaviours that generate adult cardiac structure, revealing clonal dominance as a key mechanism that shapes a vertebrate organ.