We describe, in a system whose uniqueness is that the presence of pores allows the volume to vary as budding proceeds, how phase separation on the surface of spheres extrudes material in the process called "budding". The system is giant phospholipid vesicles (GUVs) containing phase-separated regions of DOPC (soft, liquid) and DPPC (stiff, gel), with cholesterol and without it. Budding is triggered by adding the cationic pore-forming peptide, melittin. Without cholesterol, fluorescence experiments show that melittin selectively binds to the liquid domains, inducing them to form mainly exocytotic monodisperse smaller vesicle buds of this same material, causing the parent GUV to shrink. The effect of cholesterol is to produce just a few large buds following domain coalescence, rather than numerous smaller monodisperse ones. Line tension is experimentally shown to be essential for budding in this multicomponent membrane.