Today we will look at the form भौमः mNs from श्रीमद्भागवतम् 10.59.21.

शूलं भौमोऽच्युतं हन्तुमाददे वितथोद्यमः । तद्विसर्गात्पूर्वमेव नरकस्य शिरो हरिः । अपाहरद्गजस्थस्य चक्रेण क्षुरनेमिना ।। १०-५९-२१ ।।
सकुण्डलं चारुकिरीटभूषणं बभौ पृथिव्यां पतितं समुज्ज्वलत् । हाहेति साध्वित्यृषयः सुरेश्वरा माल्यैर्मुकुन्दं विकिरन्त ईडिरे ।। १०-५९-२२ ।।

श्रीधर-स्वामि-टीका –
गरुडे वितथोद्यमः सन् शूलं त्रिशूलमाददे धृतवान् ।। २१ ।। २२ ।।

Gita Press translation – His attempt having proved futile, Naraka (son of Mother Earth) picked up a pike with intent to strike at Śrī Kṛṣṇa. (But) before he could discharge it, Śrī Kṛṣṇa with his discus (Sudarśana), which was keen-edged as a razor, lopped up the head of Naraka, who rode on an elephant (21). Fallen on the ground, Naraka’s head, which was accompanied with a pair of ear-rings and adorned with a lovely diadem, shone most resplendent. “Oh, what a pity!” cried his people and “Bravo!” exclaimed the seers; while the chiefs of gods extolled Śrī Kṛṣṇa (the Bestower of Liberation,) covering Him with (a shower of) flowers (22).

The above verses have previously appeared in the following post – गजस्थस्य-mgs

भूमेरपत्यम् (पुमान्) = भौमः – a (male) descendant of Mother Earth. Here it refers to Naraka (son of Mother Earth).
Note: Depending on the context, भौमः could also refer to मङ्गलः (the planet Mars).
In the verses the विवक्षा is प्रथमा-एकवचनम्।

(1) भूमि ङस् + अण् । By 4-1-112 शिवादिभ्योऽण् – To denote the sense of अपत्यम् (descendant) the तद्धित: affix ‘अण्’ may be applied optionally following a syntactically related पदम् in which the सन्धिः operations have been performed, provided the पदम् ends in a sixth case affix and has ‘शिव’ etc (listed in the शिवादि-गण:) as its base.
Note: First the सूत्रम् 4-1-83 प्राग्दीव्यतोऽण् prescribes the default affix ‘अण्’ which is over-ruled by the affix ‘ढक्’ (prescribed by the सूत्रम् 4-1-120 स्त्रीभ्यो ढक्) and finally the सूत्रम् 4-1-112 शिवादिभ्योऽण् re-prescribes the affix ‘अण्’ because ‘भूमि’ is specifically listed in the शिवादि-गण:।
Note: The अनुवृत्तिः of ‘गोत्रे’ from the सूत्रम् 4-1-98 गोत्रे कुञ्जादिभ्यश्च्फञ् does not come into this सूत्रम् 4-1-112. It stops at the prior सूत्रम् 4-1-111 भर्गात्‌ त्रैगर्ते।
As per the सूत्रम् 4-1-92 तस्यापत्यम् – Following a syntactically related पदम् in which the सन्धिः operations have been performed and which ends in a sixth case affix the तद्धिता: affixes already prescribed (by the prior rules 4-1-83 प्राग्दीव्यतोऽण् etc), as well as those that are going to be prescribed (by the following rules 4-1-95 अत इञ् etc), may be optionally applied to denote the sense of अपत्यम् (descendant.)

(2) भूमि ङस् + अ । अनुबन्ध-लोपः by 1-3-3 हलन्त्यम्, 1-3-9 तस्य लोपः।

Note: ‘भूमि ङस् + अ’ gets the designation प्रातिपदिकम्‌ by 1-2-46 कृत्तद्धितसमासाश्च। This allows 2-4-71 सुपो धातुप्रातिपदिकयोः to apply in the next step.

(3) भूमि + अ । By 2-4-71 सुपो धातुप्रातिपदिकयोः – A सुँप् affix takes a लुक् elision when it is a part of a धातुः or a प्रातिपदिकम्।

Note: The affix ‘अण्’ is a णित् (has the letter ‘ण्’ as इत्)। This allows 7-2-117 तद्धितेष्वचामादेः to apply in the next step.

(4) भौमि + अ । By 7-2-117 तद्धितेष्वचामादेः – The first vowel among the vowels of a अङ्गम् which is followed by a तद्धित: affix (ref. 4-1-76 तद्धिताः) which is either a ञित् (has the letter ‘ञ्’ as a इत्) or a णित् (has the letter ‘ण्’ as a इत्) takes the वृद्धि: (ref. 1-1-1 वृद्धिरादैच्) substitute.

Note: The अङ्गम् ‘भौमि’ gets the भ-सञ्ज्ञा by 1-4-18 यचि भम् which allows 6-4-148 यस्येति च to apply in the next step.

(5) भौम् + अ । By 6-4-148 यस्येति च – When the letter ‘ई’ or a ‘तद्धित’ affix follows, the (ending) इ-वर्ण: (letter ‘इ’ or ‘ई’) or the (ending) अवर्ण: (letter ‘अ’ or ‘आ’) of the अङ्गम् with the भ-सञ्ज्ञा takes elision (लोपः)।

= भौम । The प्रातिपदिकम् ‘भौम’ declines like राम-शब्दः।

(6) भौम + सुँ । By 4-1-2 स्वौजसमौट्छष्टाभ्याम्भिस्ङेभ्याम्भ्यस्ङसिँभ्याम्भ्यस्ङसोसाम्ङ्योस्सुप्।

(7) भौम + स् । अनुबन्ध-लोपः by 1-3-2 उपदेशेऽजनुनासिक इत् and 1-3-9 तस्य लोपः।

(8) भौमः । रुँत्व-विसर्गौ by 8-2-66 ससजुषो रुः and 8-3-15 खरवसानयोर्विसर्जनीयः।

We can similarly derive the following –
१) इलाया अपत्यम् (पुमान्) = ऐलः (पुरूरवाः) – a (male) descendant of Ilā. It refers to Purūravā