Śrīla Rūpa Gosvāmī has described svayaṁ-rūpa in his Laghu-bhāgavatāmṛta, pūrva-khaṇḍa, verse 12, ananyāpekṣi yad rūpaṁ svayaṁ-rūpaḥ sa ucyate: the original form of the Supreme Personality of Godhead does not depend on other forms. The original form is called svayaṁ-rūpa, and it is described in Śrīmad-Bhāgavatam: kṛṣṇas tu bhagavān svayam (1.3.28). Kṛṣṇa's original form as a cowherd boy in Vṛndāvana is called svayaṁ-rūpa. It is confirmed in the Brahma-saṁhitā (5.1):

īśvaraḥ paramaḥ kṛṣṇaḥ
sac-cid-ānanda-vigrahaḥ
anādir ādir govindaḥ
sarva-kāraṇa-kāraṇam

There is nothing superior to Govinda. He is the ultimate source and the cause of all causes. In Bhagavad-gītā (7.7) the Lord says, mattaḥ parataraṁ nānyat: "There is no truth superior to Me.

The tad-ekātma-rūpa is also described in the Laghu-bhāgavatāmṛta, Pūrva-khaṇḍa, verse 14:

yad rūpaṁ tad-abhedena
svarūpeṇa virājate
ākṛtyādibhir anyādṛk
sa tad-ekātma-rūpakaḥ

The tad-ekātma-rūpa forms exist simultaneously with the svayaṁ-rūpa form and are nondifferent. At the same time, the bodily features and specific activities appear to be different. This tad-ekātma-rūpa is also divided into two categories-svāṁśa and vilāsa.

His āveśa form is also explained in the Laghu-bhāgavatāmṛta, verse 18:

jñāna-śaktyādi-kalayā
yatrāviṣṭo janārdanaḥ
ta āveśā nigadyante
jīvā eva mahattamāḥ

A living entity who is specifically empowered by the Lord with knowledge or strength is technically called āveśa-rūpa. As stated in the Caitanya-caritāmṛta (Antya 7.11), kṛṣṇa-śakti vinā nahe tāra pravartana: unless a devotee is specifically empowered by the Lord, he cannot preach the holy name of the Lord all over the world. This is an explanation of the word āveśa-rūpa.