Taṉimayam is a classical Tamil theological term built on taṉi ('single/alone/incomparable') + the abstract suffix -mayam ('full of / pervaded by'), yielding 'aloneness', 'singularity', or 'the state of being utterly alone/incomparable'. The term operates at two primary levels in Śrī Vaiṣṇava literature.
In the devotional register, taṉimayam describes the condition of Nammāzhvār in the Tiruvāymozhi during the experience of viraha (separation from Bhagavān). The Āzhvār, having once tasted the immediate experience of Bhagavān's presence (anubhava), cannot bear His absence. This results in a state of taṉimayam — a felt aloneness so absolute that neither the natural world, nor people, nor celestial beings offer any consolation. Pūrvācāryas describe this state as paradoxically the most intense form of devotion: the soul's inability to rest in anything other than Bhagavān is itself testimony to the depth of its orientation toward Him. Tirumangai Āzhvār, Āndāḷ in the Nācciyār Tirumozhi, and other Āzhvārs also describe analogous states of viraha-taṉimayam.
In the metaphysical register, taṉimayam refers to Bhagavān's incomparable uniqueness — His absolute soleness as the only self-sufficient, independent being. Bhagavān alone is svataḥ-siddha (self-established), nirāpekṣa (without dependence on anything external), and anādi-ananta (without beginning or end). All other beings — even liberated souls in Śrīvaikuṇṭha — exist in relational dependence on Bhagavān. In this sense Bhagavān's taṉimayam is the metaphysical ground of His śeṣitva (lordship over all śeṣas). The Āzhvār's experience of taṉimayam in separation is thus a mirror-image of Bhagavān's own ultimate aloneness — the only true taṉi is Bhagavān; and the soul that loves Him participates in that aloneness when separated from Him.