Who is Param Brahma or Parampita Parmeshwar?
What is the relation of lord Vishnu, lord Shankara with Param Bhrahma ?
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Brahman is that supreme entity from which everything originates, in which everything stays and into which upon desolation everything merges:
janmadasya yatah [BrSu -1.1.2]
- From whihc origin etc. take place.
yato vā imāni bhūtāni jāyante yena jātāni jīvanti yatprayantyabhisaṃviśanti tadvijijñāsasva tadbrahmeti [Tait. Up. - 3.1]
That from which all these beings are born, having born by which they live, That into which having departed they enter, seek to know That, That is Brahman.
That Brahman is both formless and with form (dve vāva brahmaṇo rūpe, mūrtaṃ caivāmūrtaṃ ca [Brh. Up. - 2.3.1]). Because we are endowed with form, we generally attribute the above three activities of creation, preservation and desolation to three different forms of the same supreme Brahman known as Brahma, Vishnu and Shiva. But Brahman is one without a second (ekam advitiyam brahman [Chg. Up - 6.2.1])and all these three are swaansha (part of the same God) or different temperaments of the same supreme entity.
So depending upon one's nature and belief people accept either Vishnu or Shiva as the supreme entity. But they are but the same. Also, the Bhagavad Gita states Shri Krishna as the parambrahman:
paraṁ brahma paraṁ dhāma pavitraṁ paramaṁ bhavān
puruṣaṁ śāśvataṁ divyam ādi-devam ajaṁ vibhum
āhus tvām ṛṣayaḥ sarve devarṣir nāradas tathā
asito devalo vyāsaḥ svayaṁ caiva bravīṣi me [BG - 10.12,13]
You are the Supreme Brahman, the ultimate abode, the purest, the Absolute Truth. You are the eternal, transcendental, original person, the unborn, the greatest. All the great sages such as Nārada, Asita, Devala and Vyāsa conﬁrm this truth about You, and now You Yourself are declaring it to me.
Another thing is that, the word Brahman in Sanskrit means an entity which is big itself and makes others big:
yasmācca bṛhati bṛṃhayati ca sarvaṃ tasmāducyate paraṃbrahmeti [Shandilya Up. - 3.2]
— Because He increases and caused everything to increase, it is called supreme Brahman.
So it's generally the same whether we say Brahman or Parambrahman. But because in Vedas, even jiva and prkruti have been termed as Brahman, when we say Parambrahman it means the supreme entity that rules over these other kinds of Brahman, namely the jiva and prakruti.
There are five separate elements in Hindu Philosophy- Jiva, Ishwara, Maya, Akshara Bramha and Para Bramha.
Jiva and Ishwara are within Maya, the two elements beyond Maya are Akshara Bramhan and Para Bramha, but please note that Bramha, Vishnu and Mahesh are like caretakers of each universe that Parabramha creates. Para Brahma creates infinite Universes and each Universe has it's own Brahma, Vishnu and Mahesh.
Akshara Bramha is the "dham" of Para Bramha, who has a very particular form and is in no way formless. Note that Bramha in trio and Akshara Bramha which is sometimes referred to as Bramha are two entirely different elements. Every universe has a Brahma while Akshara Bramha is one and irreplaceable and Para Bramha is the the reason for all reasons.
Both Akshara Bramha and Para Bramha have a specific form and Para Bramha has two forms and they are "Anvay" and "Vyeterat". Anvay is Him residing in every Jiva as Jiva is in body and Vyerate is his specific form in his Akshardham.
In Upanishads, it is said that Para Bramha is devoid of hands and feet, that is mayak hands and feet. It is said to represent that Para Bramha is an entirely different elements who has a form like that of a 17 yr old man and dark in skin tone but extremely luminous, self luminous.
So to answer your question, if Bramha, Vishnu and Mahesh are like rulers of states of India, Para Bramha is like the king of the galaxy.