Gen 12 if you don't mind?
I was hoping you'd pick this! Gen. 15 is a puzzlement, likely post-P, and Gen. 17 is P. Anyway, back to Gen. 12.
Joel Baden has published an interesting book on this, it was published after I did my research so haven't gotten around to it yet. Also try to get hold of J A Emerton's 'The origin if the promises to the Patriarchs in the older sources of the Book of Genesis'.
Traditionally Gen. 12 was attributed to J. Historically this is an original story of how Israel obtained the land, distinct from the exodus-conquest story. The earliest narrative is:
The Lord had said to Abram, Go from your country, your people and your fathers household to the land I will show you. So Abram went, as the Lord had told him. He took his wife Sarai, his nephew Lot, all the possessions they had accumulated and the people they had acquired in Harran, and they set out for the land of Canaan, and they arrived there. Abram traveled through the land as far as the site of the great tree of Moreh at Shechem. The Lord appeared to Abram and said, To your offspring I will give this land. From there he went on toward the hills east of Bethel and pitched his tent, with Bethel on the west and Ai on the east. There he built an altar to the Lord and called on the name of the Lord.
This reconstruction is an early layer, probably originating from the cult at Bethel preserved in the Northern Kingdom of Israel.
At some point the promise was added:
I will make you into a great nation,
and I will bless you;
I will make your name great,
and you will be a blessing.
I will bless those who bless you,
and whoever curses you I will curse;
and all peoples on earth
will be blessed through you.
This reflects royal theology and so could plausibly date to the monarchy, especially when Judah was under threat from Assyria. However, I am more persuaded that it was added during the exile under the influence of Second Isaiah (Isa. 40-55) since it democratises royal theology and serves to offer hope of return to the exiles.