This is probably Accelerando by Charles Stross, or possibly "Halo", one of the stories that made it up (the novel was a fix-up of stories which were individually serialized earlier).
Summary of "Halo" from the Wikipedia page:
A decade later, Amber Macx —now in her early teens— finally breaks free from her domineering mother by utilising a complex plot, thought up by Manfred and Annette, in which she enslaves herself via a Yemeni shell corporation and later enlists aboard a Franklin Collective-owned, youth-crewed spacecraft, mining materials from Amalthea, Jupiter's third moon. Pamela petitions the imam Sadeq to issue an Islamic legal judgment against Amber, which she thwarts by setting up her own empire on a small, privately owned asteroid, thus making herself sovereign. In the meantime, the alien signals have been decoded, and a physical journey to a mentioned "router" is planned.
The series as a whole are linked by the members of the Macx family who are accompanied (and perhaps in some instances guided by) Aineko, a robotic cat that Manfred Macx upgraded early on and later began upgrading itself.
The author made the entire novel available on his website for free in a variety of ebook formats, so you can check it out here if you'd like.