Jaime's in the kingsguard so he can't take it, Cersei's a woman, and it'll be a hot day on the wall before Tywin willingly lets Tyrion inherit Casterly Rock. He doesn't remarry after Joanna passes, and it doesn't seem like him to let his brother or nephew inherit the rock. So what was his plan for House Lannister and Casterly rock?
(Warhammer Fantasy)Oh mighty, Settra... Great King, the Imperishable, Khemrikhara, The Great King of Nehekhara, King of Kings, Opener of the Way, Wielder of the Divine Flame, Punisher of Nomads, The Great Unifier, Commander of the Golden Legion, Sacred of Appearance, Bringer of Light, Father of Hawks, Builder of Cities, Protector of the Two Worlds, Keeper of the Hours, Chosen of Ptra, High Steward of the Horizon, Sailor of the Great Vitae, Sentinel of the Two Realms, The Undisputed, Begetter of the Begat, Scourge of the Faithless, Carrion-feeder, First of the Charnel Valley, Rider of the Sacred Chariot, Vanquisher of Vermin, Champion of the Death Arena, Mighty Lion of the Infinite Desert, Emperor of the Shifting Sands, He Who Holds The Sceptre, Great Hawk Of The Heavens, Arch-Sultan of Atalan, Waker of the Hierotitan, Monarch of the Sky, Majestic Emperor of the Shifting Sands, Champion of the Desert Gods, Breaker of the Ogre Clans, Builder of the Great Pyramid, Terror of the Living, Master of the Never-Ending Horizon, Master of the Necropolises, Taker of Souls, Tyrant to the Foolish, Bearer of Ptra's Holy Blade, Scion of Usirian, Scion of Nehek, The Great, Chaser of Nightmares, Keeper of the Royal Herat, Founder of the Mortuary Cult, Banisher of the Grand Hierophant, High Lord Admiral of the Deathfleets, Guardian of the Charnal Pass, Tamer of the Liche King, Unliving Jackal Lord, Dismisser of the Warrior Queen, Charioteer of the Gods, He Who Does Not Serve, Slayer off Reddittras, Scarab Purger, Favoured of Usirian, Player of the Great Game, Liberator of Life, Lord Sand, Wrangler of Scorpions, Emperor of the Dunes, Eternal Sovereign of Khemri's Legions, Seneschal of the Great Sandy Desert, Curserer of the Living, Regent of the Eastern Mountains, Warden of the Eternal Necropolis, Herald of all Heralds, Caller of the Bitter Wind, God-Tamer, Master of the Mortis River, Guardian of the Dead, Great Keeper of the Obelisks, Deacon of the Ash River, Belated of Wakers, General of the Mighty Frame, Summoner of Sandstorms, Master of all Necrotects, Prince of Dust, Tyrant of Araby, Purger of the Greenskin Breathers, Killer of the False God's Champions, Tyrant of the Gold Dunes, Golden Bone Lord, Avenger of the Dead, Carrion Master, Eternal Warden of Nehek's Lands, Breaker of Djaf's Bonds... and many, many more...
(ASOIAF)Daenerys Stormborn of the House Targaryen, First of Her Name, the Unburnt, Queen of Meereen, Queen of the Andals and the Rhoynar and the First Men, Khaleesi of the Great Grass Sea, Breaker of Chains, and Mother of Dragons.
(IRL)
Blade of Gaia (Warhammer 40k meme)
The ring is made of human sized viltrumite bodies, I don't know how big viltrum is or if there is even a canonical answer, but if there isn't lets assume it's earth sized.