In regard to the movements and residences of the dwarves:
Here is an excerpt from a leter essay of Tolkien's CT named: Of Dwarves and Men and published in The Peoples of Middle-earth(HoME XII):
Quote:
In the Dwarvish traditions of the Third Age the names of the places where each of the Seven Ancestors had 'awakened' were remembered; but only two of them were known to Elves and Men of the West: the most westerly, the awakening place of the ancestors of the firebeards and Broadbeams; and that of the ancestors of the Longbeards, the eldest in making and awakening. The first had been in the north of Ered Lindon, the great eastern wall of Beleriand, of which the Blue Mountains of the Second and later ages were the remnant; the second had been Mount Gundabad(in origin a Khuzdul name), which was therefore revered by the Dwarves, and its occupation in the Third Age by the Orks of Sauron was one of the cheif reasons for their great hatred of the Orks. The other two places were eastward, at distances as great or greater than that between the Blue Mountains and Gundabad: the arising of the Ironfists and Stiffbeards, and that of the Blackflocks and Stonefoots. Though these four points were far sundered the Dwarves of different kindreds were in communication and in the earley ages often held assemblies of delegates at Mount Gundabad. In times of great need even the most distant would send help to any of their people; as was the case in the great War against the Orks (Third Age 2793 to 2799). Though they were loth to migrate and make permanent dwellings or 'mansions' far from their original homes, except under great pressure from enemies or after some catastrophe such as the ruin of Beleriand, they were great and hardy travellers and skilled road-makers; also all the kindreds shared a common language. -pg 301
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As Tolkien seems to allude to in the above it does seem after the destruction of Beleriand at the end the First age the Firebeards and Broadbeams migrated west to Moria as is stated in Appendix A & B:
[/quote]After the end of the First Age the power and wealth of Khazad-dûm was much increased; for it was enriched by many people and much lore and craft when the ancient cities of Nogrod and Belegost in the Blue Mountains were ruined at the breaking of Thangorodrim. -Appendix A[/quote]
Quote:
c.40[S.A.] Many Dwarves leaving their old cities in Ered Luin go to Moria and swell its numbers. -Appendix B
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Therefore it seems that a combination of Longbeards, Firebeards and Broadbeams lived in Moria.
After the awakening of the Balrog and the flight from Moria in 1980-1(T.A.) this polyglot seems to have dispersed a bit mainly to The Grey Mountains in the North and the also to what would be 'the Kingdom under the Mountain'(1999):
[/quote]Most of these that escaped made their way into the North, and Thróin I, Náin's son, came to Erebor, the Lonely Mountain, near the eastern eaves of Mirkwood, and there he began new works, and became King under the Mountain. -Appendix A[/quote]
The majory of those in the North do seem to have been counted among the Longbeards or rather the majority of the Longbeards went north as they are refered to as 'Durin's Folk':
Quote:
But Thorin I his son removed and went into the far North to the Grey Mountains, where most of Durin's folk were now gathering... -Appendix A
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Then after the attacks of the cold drakes(Dáin father of Grór and Thrór was killed in 2589) it does appear most fled to the Iron Hills with Grór and to Erebor with Thrórin:
Quote:
Not long after most of Durin's Folk abandoned the Grey Mountains. Grór, Dáin's son, went away with many followers to the Iron Hills; but Thrór, Dáin's heir, with Borin his father's brother and the remainder of the people returned to Erebor.
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then when the Kingdom under the mountain was taken by Smaug(2770) most traveled south to the Iron Hills though some went wandering with Thrain and Thorin (Oakensheild):
Quote:
It was afterwards learned that more of the Folk under the Mountain had escaped than was at first hoped; but most of these went to the Iron Hills -footnote to Appendix A
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Then later after the Battle of five Armies in 2941 the dwarven Kingdom under the Mountain was reestablished and later after the War of the Ring Gimli established a kingdom in the Glittering Caves:
Quote:
After the fall of Sauron, Gimli brought south a part of the Dwarf-folk of Erebor, and he became Lord of the Glittering Caves. Appendix A
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Changing now to the issue of the Ironfists and Stiffbeards; and the Blackflocks and Stonefoots in the east I think given again:
Quote:
...they were loth to migrate and make permanent dwellings or 'mansions' far from their original homes, except under great pressure...(HoME 12)
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I think we can assume that they probably held 'permanent' residences somewhere in the east.
So in the Third Age(the major areas of inhabitation):
1-1981
- Longbeards, Firebeards and Broadbeams- live mostly in Moria(F&B from Belegost and Nogrod)
- Ironfists and Stiffbeards- probably somewhere in the far East
- Blackflocks and Stonefoots -probably somewhere in the far East
1981-2589
- Longbeards(the majority['most']), Firebeards and Broadbeams- The Grey Mountains
- Longbeards, Firebeards and Broadbeams - Erebor('kindom under the mountain'[1999])
- Ironfists and Stiffbeards- probably somewhere in the far East
- Blackflocks and Stonefoots -probably somewhere in the far East
2589-2770
- Longbeards), Firebeards and Broadbeams- Erebor('kindom under the mountain')
- Longbeards, Firebeards and Broadbeams - The Iron Hills(2590)
- Ironfists and Stiffbeards- probably somewhere in the far East
- Blackflocks and Stonefoots -probably somewhere in the far East
2770-2941(reign of smaug)
- Longbeards, Firebeards and Broadbeams - The Iron Hills
- Longbeards, Firebeards and Broadbeams - apparently some few returned to the blue mountian mansions
- Ironfists and Stiffbeards- probably somewhere in the far East
- Blackflocks and Stonefoots -probably somewhere in the far East
2941-~3019
- Longbeards), Firebeards and Broadbeams- Erebor reestablished('kindom under the mountain')
- Longbeards, Firebeards and Broadbeams - The Iron Hills
- Ironfists and Stiffbeards- probably somewhere in the far East
- Blackflocks and Stonefoots -probably somewhere in the far East
3019<
- Longbeards), Firebeards and Broadbeams- Erebor('kindom under the mountain')
- Longbeards, Firebeards and Broadbeams - The Iron Hills
- Longbeards, Firebeards and Broadbeams - The Glittering Caves
- Longbeards- possibly moria given what is said by Dáin after the Dwarven-Goblin War*
- Ironfists and Stiffbeards- probably somewhere in the far East
- Blackflocks and Stonefoots -probably somewhere in the far East
*"...The World must change and some other power than ours must come beofre Durin's Folk walk again in Moria." -Appendix A