The word adhirāja (adhiraja) does not merely define a king ruling over a populated geographical locale. Rather adhirāja is a king who has conquered even other kingdoms and has established his indisputable power. In one particular hymn of Ṛgveda (Rigveda), the second incantation reads as a prayer, “Let all four directions bow down to me, let me defeat all my enemies”— mahyaṃ namantāṃ pradiśaścatasraḥ.
This hymn ends with the prayer— “let me prevail over everyone, let me be adhirāja”— uparispṛśam…adhirājamakran.
Śatapatha Brāhmaṇa (Shatapatha Brahmana) clarifies that the title of adhirāja signifies a prestigious stature over many kings. Here, it is said that adhirāja is “the supreme one among kṣatriyas, the king over/superior to other kings”— kṣatrānāṃ kṣatrapatiredhīti rājñām adhirāja….
Brahmāṇḍapurāṇa (Brahmandapurana) further states that ever since the first ever rightful king of the earth, Pṛthu (Prithu) was crowned king at the Rājasūya yajña (yajna), he was ordained by the term adhirāja —
vedadṛṣṭena vidhinā hyadhi rājaḥ pratāpavān.
Like svarāṭ (swarat), samrāṭ (samrat), ekarāṭ (ekarat), et al, adhirāja, too, is a distinguished appellative.