  From Gross-Pitaevskii (GP) theory for ultracold gases it is predicted that
phase-segregated three-component Bose-Einstein condensates (BEC) feature a
wetting phase diagram that depends only on atomic masses and scattering
lengths. This is unique in theories of surface and interfacial phase
transitions and provides a new opportunity for experimental observation of
wetting phenomena in BEC mixtures. Previous GP theory for two-component BEC
relied on an {\it ad hoc} optical wall boundary condition, on which the
character and location of the wetting phase transitions depend sensitively.
This boundary condition dependence is eliminated by adding a third component
and treating the three phases on equal footing. An unequivocal wetting phase
diagram is captured, with phase boundaries calculated analytically using an
extension of the established double-parabola approximation.
