Epitaxial films of the archetypical bubble garnet (R, Y)3Fe5O12, where R is a rare earth, were grown on (111) Gd3Ga5O12 substrates from a 200:1 by weight PbO:B2O3 flux using the horizontal dipping technique with rotation. Growth rate was varied by adjusting supercooling and rotation rate, and the equilibrium segregation coefficients of the dodecahedrally crystallizing cations KR = Rxtal/Rmelt were determined with reference to the film-lattice constant and the segregation of these cations on octahedral sites. KR was found to obey the growth model of Burton, Prim, and Slichter [J. Chem. Phys. 21, 1987 (1953)], KR = KR0/[KR0+(1−KR0)e−kf], where f is the growth rate, KR0 is the segregation coefficient at zero growth rate, and k is a parameter which is a function of the thickness of the growth interface and the diffusion constant. The parameter k was found to be independent of the species R and to have the value 1.18 sec μm−1 for the particular growth condition. A strong correlation was found between KR0 and the partial molar heat of mixing of the R2O3 oxide and the flux, as calculated from regular solution theory [D. M. Gualtieri, J. Appl. Phys. 50, 2170 (1979)].