how would we aerobreak it in mars's atmosphere into a decaying orbit, so instead of slamming into mars, it breaks up and rains down on mars? What can we tell about the composition - a solid rock or icy rubble?
The martian atmosphere will have a negligible impact on a 200km wide object. Tidal forces would likely shred the object and the surface of Mars if an aerobraking maneuver was attempted.
Shouldn't break by itself with Mars' tidal forces alone?
You get it into an orbit that will have several close encounters with Mars or other planets with atmosphere and you do a bit of aerobraking/thrusting on each pass.