Moorthitraya means the three entities of Divinity; each entity demarcated for one function. The three moorthis or forms denoted as Baba's Swarupa (real nature) are Brahma, Vishnu and Shiva, the Entities responsible for Creation, Protection and Destruction. Emergence, Existence and Mergence; Source, Stream and Sea; Srishthi, Sthithi and Laya. Baba has all Three, is all Three. He creates objects from nothing. He preserves objects without diminution or decline (vide: His granting containers full of Vibhoothi or Kumkum which never become empty, however fast you use them). He dissolves objects into nothing.
Since He is all the three, He is called as Dattatreya. He is 'Thatkshanaath Sarva Gami' (reaching everywhere immediately) and 'Thyagi (detached) Bhogi (consuming objects, as the Indweller of all who consume) Divyayogi (the divine unifier) and Dayalu (full of mercy and grace). Sai Baba is the Incarnation of the Dattatreya form of Sri Narayana and so Sathya Sai Baba is Moorthi-thraya Swarupa. He creates; He preserves; He subsumes.