One of the cool things about the Moon is that the far side has a thicker crust that the near side.1 One theory explaining this is that the Moon was hit by an object, possibly a moonlet created by the remains of Theia as per the Giant Impact Hypothesis (while the Moon was still forming). The object hit in such a way that more material was deposited than was blown away, leading to the thicker crust.
Let's say I own an interstellar mining company, and I've come across a system with plenty to spare. There are four rocky planets orbiting a central Sun-like star. There's also an asteroid belt at between 3 and 4 AU, with a total density (i.e. number density of asteroids multiplied by the mass of each asteroid) of about three times that of the asteroid belt in our Solar System.
I don't want to mine each asteroid directly because that would require some major infrastructure problems. However, I've figured out that I might be able to divert some of the asteroids towards the planet, which lies at 2.5 AU. If I get it just right, I might be able to move some asteroids close enough to leave a lot of mineable material. Then I can swoop in and set up shop.
The issue is, too many impacts could cause a whole bunch of issues for the planet, making it worthless. And too many impacts could damage the material already there. At the same time, I want to get as much material as possible deposited onto the planet.
Assuming I can divert a large number of asteroids away via some as-yet-undetermined (but not precise) method, how many should I send in the direction of the planet to maximize my yield? Note that I'll need a large asteroid flux (in terms of number density) because many could and will completely miss.
A potentially useful paper is Asteroid and comet flux in the vicinity of Earth (Shoemaker et al, 1990).
I'd like answers to focus on how much material could be deposited on each impact, orbital perturbations of the planet, regional distribution of impacts (due to planetary rotation) and how they can impact mineability of deposited material, and asteroid flux. Answers discussing only one or two factors, however, will be much appreciated; you don't need to cover everything to write a high-quality answer.