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The sudden removal of Jupiter would not be pleasant for the Trojan asteroids located at the Lagrangian points on Jupiter's orbit. The various asteroids that are in resonance orbits with Jupiter would also be ultimately affected - i.e. no longer in resonance lock. There will also be a considerable effect on the interlopers from the nether regions such as comets.
The interesting thing over time will be upon the nature of what outer solar system debris will make their way into the inner solar system i.e. the giant "hoover" being removed I suspect means greater chance of the Earth being hit by something.
If you Google "centre of mass of the solar system" you'll find some more information regarding what effect each of the planets has upon the solar system's COM point.
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