  By combining Monte Carlo simulations and analytical models, we demonstrate
and explain how the gas-to-liquid phase transition of colloidal systems
confined to a spherical surface depends on the curvature and size of the
surface, and on the choice of thermodynamic ensemble. We find that the geometry
of the surface affects the shape of the free energy profile and the size of the
critical nucleus by altering the perimeter-area ratio of isotropic clusters.
Confinement to a smaller spherical surface results in both a lower nucleation
barrier and a smaller critical nucleus size. Furthermore, the liquid domain
does not grow indefinitely on a sphere. Saturation of the liquid density in the
grand canonical ensemble and the depletion of the gas phase in the canonical
ensemble lead to a minimum in the free energy profile, with a sharp increase in
free energy for additional growth beyond this minimum.
