If baryosynthesis is strongly nonhomogeneous, macroscopic regions with antibaryon excess can be created in the same process from which the baryonic matter is originated. This exotic possibility can become real, if the hints to the existence of antihelium component in cosmic rays are confirmed in the AMS02 experiment, indicating the existence of primordial antimatter objects in our Galaxy. Possible forms of such objects depend on the parameters of models of baryosynthesis and evolution of antimatter domains. We elaborate the formalism of analysis of evolution of antibaryon domain with the account for baryon-antibaryon annihilation at the domain borders and possible “Swiss cheese” structure of the domain structure. We pay special attention to evolution of various forms of high, very high and ultrahigh density antibaryon domains and deduce equations of their evolution in the expanding Universe. The proposed formalism will provide the creation of evolutionary scenarios, linking the possible forms and properties of antimatter bodies in our Galaxy to the mechanisms of nonhomogeneous baryosynthesis.