Where did the Moon come from?
https://iopscience.iop.org/article/10.1086/427539/pdf
E Belbruno, JR Gott III - The Astronomical Journal, 2005
We propose that the giant impactor could have formed in a stable orbit among debris at Earth’s L4 (or L5) Lagrange point. We show that such a configuration is stable, even for a Mars-sized impactor. It could grow gradually by accretion at L4 (or L5), but eventually gravitational interactions with other growing planetesimals could kick it out into a chaotic creeping orbit, which we show would likely cause it to hit Earth on a zero-energy parabolic trajectory. We argue that this scenario is possible and should be further studied.
Jacobson, S.A. and Walsh, K.J., 2015. Earth and terrestrial planet formation. The early Earth: Accretion and differentiation, pp.49-70.
https://arxiv.org/pdf/1502.03852.pdf
The feeding zones,which determine the compositions of Earth and Venus follow a particular pattern determined by Jupiter, while the feeding zones of Mars and Theia, the last giant impactor on Earth, appear to randomly sample the terrestrial disk. Thelate accreted mass samples the disk nearly evenly.
https://www.researchgate.net/profile/E_Asphaug/publication/280321193_Impact_Origin_of_the_Moon/links/55bb9a8e08aec0e5f4418e9f.pdf
Asphaug, E., 2014. Impact origin of the Moon?. Annual Review of Earth and Planetary Sciences, 42, pp.551-578.
The idea that Earth and the Moon coaccreted as a binary pair was refined by Morishima &Watanabe (2001) in the context of the waning solar nebula. But W isotopes and other chronometers(Touboul et al. 2007) have shown that the Moon must have formed long after the disappearance of the gas, at∼4.5 Ga or later. Without the nebula, coaccretion appears impossible to support dynamically. Another idea—another kind of coaccretion—is that Theia formed at one of Earth’s Trojanpoints (Belbruno & Gott 2005) or otherwise in the same feeding zone near 1 AU. Coformationof some kind is consistent with the low-velocity collision that is required of the standard model.But even if the physical conditions could be satisfied to make a Mars-mass Trojan, it might notbe sufficient to make Theia in the same feeding zone as Earth, or in a Trojan point of Earth, togive it indistinguishable isotopes. A Trojan point exists only after Earth is substantially accreted,so it would be a depleted and much less massive region of the disk. It remains to be demonstrated how a Trojan Theia or a nearby Theia, forming at lower pressures, fugacities, and temperatures and with different boundary conditions, would have the same isotopes.