A mathadhipathi is the manager and custodian of the institution. See Vidya Varuthi Thirtha vs. Balusami Ayyar, 48 Ind App 302 at pages 311, 315. The office carries with it the right to manage and possess the endowed properties on behalf of the math and the right to sue on its behalf for the protection of those properties. During the tenure of his office, the mathadhipathi has also large beneficial interests in the math properties, see Commissioner, Hindu Religious Endowments, Madras vs. Sri Lakshmindra Thirtha Swamiar of Srirur Mutt, (1954) SCR 1005 at pages 1018-1020. But by virtue of his office, he can possess and enjoy only such properties as belong to the math.
If the title of the math to any property is extinguished by adverse possession, the rights of all beneficiaries of the math in the property are also extinguished. On his appointment, the mathadhipathi acquires no right to recover property which no longer to the math.
Ref: AIR 1966 SC 1603 : (1966) 1 SCR 908