From the second edition (1989):
their, poss. pron.
(ðɛə(r)) Forms: see below. [In existing form their, in Ormin þeȝȝre, a. ON. þeir(r)a, genitive pl. of simple demonst. , , þat (= OE. se, séo, þæt), used in ON. also as pl. of 3 pers. pron. The β-forms þer, þar, þere, etc., were prob. due mainly to the unstressed pronunciation of their, thair, confused sometimes with that of the adv. þær, thare, there; but they may sometimes represent OE. þǽra, late form of þára, gen. pl. of þá those, substituted for the same case of the personal pronoun. Cf. them.]

A. Illustration of Forms.

(α) 3 (Orm.) þeȝȝre, (teȝȝre), 4 þeir(e, þeyr, þayre, þayire, þaier, 4–5 þair, þaire, 5 þeire; 4–5 thaire, 5 thayre, 5–7 theire, theyr, 6 thayr, (thier, 6–7 yair), 4– Sc. thair, 5– their.

c1200 Ormin Ded. 84 All þurrh þeȝȝre sinne. Ibid. 3933 Þatt teȝȝre genge shollde ben Þurrh hallȝhe sawless ekedd. 1303 R. Brunne Handl. Synne 874 Þarefore þat day al holy cherche Þeyr seruyse of here þey werche. 13‥ Cursor M. 794 (Cott.) Al þaier kin. Ibid. 21800 (Edin.) Mani man‥Þate thair [v.r. þair] hele hauis getin þare. a1340 Hampole Psalter lxxvii. 51 He gaf‥þaire trauails til þe locust. c1400 Destr. Troy 6738 Menelaus, and Thelamon,‥with theire tite batels. c1440 Pallad. on Husb. i. 116 Oute of thaire [v.r. their] kynde eke seedes wol renewe. 1470–85 Malory Arthur vii. xviii. 240 All they felle vpon their knees. 1522 Rutland Papers (Camden) 84 To putt all thier stuf of householde in euery office. 1538 Starkey England i. iv. 120 To tempur and refrayne thayr malyce. 1549 Baxter-bks. St. Andrews (1903) 5 Thomas mortowne To be yair Decane. a1568 Wyfe of Auchtermuchty xii, That straik dang baith thair harnis owt. 1620 Sir R. Naunton in Fortescue Papers (Camden) 139 Theyr general aunswer to his Majesties commandement. 1641 Best Farm. Bks. (Surtees) 126 Holes, of that bignesse that one may thrust in theire neafe.

(β) (1 þæra, þeora) 4 þer, þar, (þur), 4–5 þere, 4–6 þare, thar, 5 thare, 5–6 ther, 6–8 there, 7 thir (used by Milton as unstressed form of their).

[?a1100 O.E. Chron. (Laud MS.) an. 449, On þeora daum elaðode Wyrteorn Angelcin hider. Ibid. an. 1086, Þæt þa godan men niman æfter þeora godnesse.] c1330 R. Brunne Chron. (1810) 127 Þe popille him bisouht þer kyng forto be. 13‥ Cursor M. 476 (Cott.) Þat sithen þar [v.rr. þair(e, her] sted was neuer sene. Ibid. 666 Bath he sette in þare [v.rr. þair(e, her] fre will. Ibid. 13900 Moyse þur lagh þaim broght. c1400 Destr. Troy 12467 Trees, thurgh tempestes, tynde hade þere leues. c1450 Godstow Regr. 491 Ther heires lawfully I-be-gote of ther bodies. c1460 Towneley Myst. ix. 119, I shalle fownd to crak thare crowne. 1513 Douglas Æneis iv. ix. 33– 4 The ryning fludis thar wattir stop can scho mak, And eik the sternis turne ther cours abak. 1526 There [see B. 1]. 1533 Bellenden Livy ii. xix. (S.T.S.) I. 205 Þai obeyit weill eftir to þare capitanis. 1663 Chas. II in Julia Cartwright Henrietta of Orleans (1894) 139 They will shew there affections to me. 1671 Milton P.R. ii. 235 He ceas'd, and heard thir grant in loud acclaim. 1757 E. Griffith Lett. Henry & Frances (1767) I. 56 Rogueries‥which, they thought, brought a disgrace on there bruteships.

B. Signification.

1. poss. adj. (orig. gen. pl. of pers. pron.) Of, belonging, or pertaining to them; also refl. of or belonging to themselves.

c1200 Ormin 127 Naffdenn þeȝȝ þurrh þeȝȝre streon Ne sune, child, ne dohhterr. c1330 R. Brunne Chron. Wace (Rolls) 1115 Brutus wiþ his folk‥wente þer weye. 1340 Hampole Pr. Consc. 3884 Prelats‥Sal account yhelde‥Of þair suggets undir þair powere. 1526 Tindale Matt. vi. 5 Vereley I saye vnto you they have there rewarde. 1589 Puttenham Eng. Poesie i. vi. (Arb.) 27 Vnder the conduict of Totila and Atila and other their generalles. 1617 Moryson Itin. ii. 219 Consider the inward motiues of their crauing mercy. 1640 tr. Verdere's Rom. of Rom. I. xviii. 78 With that they tooke their leaves of her. 1774 Goldsm. Nat. Hist. (1776) VI. 222 The great agility of these animals prevents their often being taken. 1797 Godwin Enquirer i. vi. 41 We must dwell upon their every word. 1847 De Quincey Orthogr. Mutineers Wks. 1860 XIV. 105 When‥he [Milton] wishes to direct a bright jet of emphasis upon the possessive pronoun their, he writes it as we now write it. But when he wishes to take off the accent, he writes it thir. [Cf. A. β 1671.] 1853 M. Arnold Empedocles ii. 19 With men thou canst not live; Their thoughts, their ways, their wishes, are not thine. 1858 O. W. Holmes Aut. Breakf.-t. iv, Long after the frost and snow have done their worst with the orchards. 1864 Tennyson Aylmer's F. 383 These old pheasant-lords‥Who had mildew'd in their thousands, doing nothing Since Egbert.

b. obj. gen. Of (for, to) them. (Cf. his B. 2.)

1553 T. Wilson Rhet. (1580) 77 For a tyme your grace muche bewailed their lacke. 1579 [see 5]. 1590 Spenser F.Q. iii. iii. 43 Shall‥quite from off the earth their memory be raste? 1607 Topsell Four-f. Beasts (1658) 66 Yet can there not be in any nation a neglect of oxen; and their reverence was so great that, in ancient time [etc]. 1780 Beckford Biog. Mem. 108 Humanity pleads strongly for the abridgment of their relation. a1912 Mod. We mourn their loss.

c. Const. with gen. pl. of all, both: their aller, their bother, their beyre (obs.); also all their, their both, both their, each of their (arch.): meaning ‘of all, both, or each of them’. See all D. 4, both 4b, bo a. c.

a1250 Owl & Night. 1584 Þe louerd‥Vareþ vt on þare beyre neode. a1300 Cursor M. 18766 He stei up in þair aller sight. c1380 Wyclif Serm. Sel. Wks. I. 289 Þe fend‥is þer alþer kyng. c1465 Eng. Chron. (Camden) 48 Be thair bothe assent. 1559 Mirr. Mag. (1563) Dv, Lo thus fond hope dyd theyr both lyues abrydge. a1568 [see A. α]. 1589 Puttenham Eng. Poesie i. viii. (Arb.) 35 Saying thus in all their hearings. 1654–66 Earl of Orrery Parthen. (1676) 550 With both their helps I was carried to a Chamber. 1672 Temple Misc. i. 64 According to each of their hunger or need. 1874 Swinburne Bothwell ii. i, Mine and all their free and sovereign king.

2. Used of a thing with which a number of persons have to do, or which is assumed to be the common possession of a class; e.g. ‘These boys know their Greek syntax’. Cf. his poss. pron. 1b.

1785 Burns Halloween ii, To burn their nits, an' pou their stocks, An' haud their Halloween. 1905 Daily Chron. 2 Sept. 3/1 All those who love their Devon and especially their Dartmoor.

3. Often used in relation to a singular n. or pronoun denoting a person, after each, every, either, neither, no one, every one, etc. Also so used instead of ‘his or her’, when the gender is inclusive or uncertain. Cf. they pron. 2, them pron. 2; nobody 1b, somebody. (Not favoured by grammarians.)

13‥ Cursor M. 389 (Cott.) Bath ware made sun and mon, Aiþer wit þer ouen light. c1420 Sir Amadace (Camden) l, Iche mon in thayre degre. 14‥ Arth. & Merl. 2440 (Kölbing) Many a Sarazen lost their liffe. 1533 [see themselves 5]. 1545 Abp. Parker Let. to Bp. Gardiner 8 May, Thus was it agreed among us that every president should assemble their companies. 1563 Winȝet Four Scoir Thre Quest. liv, A man or woman being lang absent fra thair party. 1641 [see A. α]. 1643 Trapp Comm. Gen. xxiv. 22 Each Countrey hath their fashions, and garnishes. 1749 Fielding Tom Jones vii. xiv, Every one in the House were in their Beds. 1771 Goldsm. Hist. Eng. III. 241 Every person‥now recovered their liberty. a1845 Syd. Smith Wks. (1850) 175 Every human being must do something with their existence. 1848 Thackeray Van. Fair xli, A person can't help their birth. 1858 Bagehot Lit. Studies (1879) II. 206 Nobody in their senses would describe Gray's ‘Elegy’ as [etc.]. 1898 G. B. Shaw Plays II. Candida 86 It's enough to drive anyone out of their senses.

4. After a n. (usually a proper name), instead of the genitive inflexion. Cf. his poss. pron. 4, her poss. pron. 3rd pl. 3. Obs. or rare arch.

1551 Robinson tr. More's Utop. ii. (1895) 172 Vntyll the vtopians their creditours demaunde it. 1600 Shakspere's Titus A. (title-p.), As it hath sundry times beene playde by the Right Honourable the Earle of Pembrooke,‥and the Lorde Chamberlaine theyr Seruants. 1642 Featley Dippers Dipt (1646) 11 These travellers their report, and the testimony of those witnesses. 1642 Drummond of Hawthornden Skiamachia Wks. (1711) 193 An answer to the parliament of England their declaration. 1667 Pepys Diary 3 Jan., The House of Lords their proceedings in petitioning the King. 1681 R. Burthogge Argt. for Inf. Bapt. (1684) 6 From the Children of Believers their being Abraham's Spiritual Seed.

5. Serving as antecedent to a following relative; equivalent to ‘of those’. (Now usually avoided.)

1579 Tomson Calvin's Serm. Tim. 134/2 Under their obedience whome God hath set ouer us. 1593 in J. Morris Troubles Cath. Forefathers Ser. iii. (1877) 124 The chiefest favour must be procured by their means that have spoiled us before. 1655 Fuller Ch. Hist. ix. vii. §14 This prediction‥yet miss'd their meaning, who both first reported, and most believed it.

6. absol. = theirs. Cf. her poss. pron. 3rd pers. pl. 4. Obs.

13‥ Cursor M. 7465 (Cott.) A man o þair gains an of vr. 1592 G. Harvey Four Lett. Wks. (Grosart) I. 216, I offer them my hande: and request their. 1618 Wither Motto Ciijb, My clothing keeps me full as warm as their [rime are]. Ibid. Civ, And my esteeme I will not change for their.