And if they're left to their own devices, the nanites will continue to alchemize every bit of matter within reach. This is the reason it's still illegal to use them in a terrestrial gravity well, despite their value to manufacturing. One recursion in the supervisory software, or one night where the operator forgets to shut things down before going home, and you wake up to a runaway gray goo scenario. A massive nodule of pure palladium in the middle of the Antarctic, where a hot lab stood not twenty-four hours before, reminded everyone rather pointedly of this, at least until the international backers of the research project almost caused a major diplomatic incident over who owned the palladium nodule.
The composition of the asteroid confirmed (large quantities of silicon compounds, nickel, and iron), the ship printers fire up and spit out a mining package of several small drones with their own seed colony of nanites. One of the drones is a mobile printer with just enough sophistication to make an identical copy of itself, at which point they step up into exponential growth for a short period of time and then get down to the real work of coring the asteroid for anything remotely useful.
One of the last activities before shoving off is the shuttling of raw mass up to the ship from the asteroid to refill the alchemy tanks back to optimal load. Using mostly silicon, iron, and nickel, it takes a lot of matter to fill the tanks, but there's plenty to go around. While the ship fills up, the first priority in the unpacking mining suite is the construction of a communications array and processor hub. Just as the alchemy tanks are topped off, the Joyeuse squirts a hundred gigs of data down to the asteroid's new “brain” in a couple seconds, followed by the system linking up to the StarGen hub back at Earth's L4.
In comparison, Sitri's drone requires an upload of a few hundred terabytes and takes just over two hours to transfer through from her PAN. And that's with some very fancy compression and a mere AI seed, rather than a full-grown AI. It's designed to run solo, though, compared to the dumb StarGen systems which are in constant (if lagged) contact with the master network. Nobody will talk to Sitri's drone for the next couple years.