Today we will look at the form भारत mVs from श्रीमद्भागवतम् 6.17.16

अतः पापीयसीं योनिमासुरीं याहि दुर्मते । यथेह भूयो महतां न कर्ता पुत्र किल्बिषम् ॥ ६-१७-१५ ॥
श्रीशुक उवाच
एवं शप्तश्चित्रकेतुर्विमानादवरुह्य सः । प्रसादयामास सतीं मूर्ध्ना नम्रेण भारत ॥ ६-१७-१६ ॥

श्रीधर-स्वामि-टीका –
तदेवं स्वयं दण्ड्यत्वं निश्चित्य तं प्राह – अत इति । हे पुत्र, यथा भूयो महतां किल्बिषमपराधं न कर्ता न करिष्यसि तथा याहीत्यर्थः ।। १५ ।। १६ ।।

Gita Press translation “Hence be reborn in the demoniac species – a most wicked species – O evil-minded one, so that you may not perpetrate again in this world, such offense against the exalted souls my son.” Śrī Śuka resumed : “Thus subjected to an execration, the said Citraketu alighted from his aerial car and propitiated the noble lady (Goddess Pārvatī) with his head bent low (in the following words), O Parīkṣit (a scion of Bharata).”

The above verses have previously appeared in the following post – कर्ता 3As-लुँट्

भरतस्यापत्यम् (पुमान्) = भारतः – a (male) descendant of Bharata – here it refers to Parīkṣit
In the verses the विवक्षा is सम्बुद्धिः, hence the form used is भारत।

(1) भरत ङस् + अञ् । By 4-1-86 उत्सादिभ्योऽञ् – The तद्धित: affix ‘अञ्’ is authorized for all rules down prior to the सूत्रम् 4-4-2 तेन दीव्यति खनति जयति जितम्, provided it is applied to a पदम् which has ‘उत्स’ etc (listed in the उत्सादि-गण:) as its base.
Note: The affix ‘अञ्’ prescribed by 4-1-86 is a अपवादः to the default affix ‘अण्’ (prescribed by the सूत्रम् 4-1-83 प्राग्दीव्यतोऽण्) as well as the affixes (‘इञ्’ etc.) which are अपवादाः to the affix ‘अण्’।
Note: The final form is the same regardless of whether the affix ‘अञ्’ (prescribed by the सूत्रम् 4-1-86) or the default affix ‘अण्’ (prescribed by 4-1-83 प्राग्दीव्यतोऽण्) is used. The only difference is in the स्वरः (intonation) in the Vedas.
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.)

Note: In the present example, first the सूत्रम् 4-1-83 प्राग्दीव्यतोऽण् prescribes the default affix ‘अण्’ which is over-ruled by the affix ‘इञ्’ (prescribed by the सूत्रम् 4-1-95 अत इञ्)। This in turn is over-ruled by the affix ‘अञ्’ (prescribed by the सूत्रम् 4-1-86 उत्सादिभ्योऽञ्) since ‘भरत’ is listed in the उत्सादि-गण:।

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

Note: ‘भरत 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) भरत + 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 ‘अञ्’ is a ञित् (has the letter ‘ञ्’ as इत्)। This allows 7-2-117 तद्धितेष्वचामादेः to apply in the next step.

(4) भारत + 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 ‘भारत’ gets the भ-सञ्ज्ञा by 1-4-18 यचि भम् which allows 6-4-148 यस्येति च to apply in the next step.

(5) भारत् + 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)।

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

The विवक्षा is सम्बुद्धिः। By 2-3-49 एकवचनं सम्बुद्धि: – The nominative singular affix (‘सुँ’) when used in a vocative form gets the designation सम्बुद्धि:।

(6) (हे) भारत + सुँ । By 4-1-2 स्वौजसमौट्छष्टाभ्याम्भिस्ङेभ्याम्भ्यस्ङसिभ्याम्भ्यस्ङसोसाम्ङ्योस्सुप्‌। By 2-3-47 सम्बोधने च – A first case affix (‘सुँ’, ‘औ’, ‘जस्’) is used to denote ‘address’ (in addition to the meaning of the nominal stem) also. Note: सम् (सम्मुखीकृत्य) बोधनम् (ज्ञापनम्) = सम्बोधनम्। सम्बोधनम् means drawing someone’s attention (to inform him/her of something.)

(7) (हे) भारत + स् । अनुबन्ध-लोप: by 1-3-2 उपदेशेऽजनुनासिक इत् and 1-3-9 तस्य लोपः।

(8) (हे) भारत । By 6-1-69 एङ्ह्रस्वात्‌ सम्बुद्धेः – Following a अङ्गम् ending in ‘एङ्’ (letter ‘ए’ or ‘ओ’) or a short vowel, a consonant is dropped if it belongs to a सम्बुद्धि: affix.