While Jupiter is the largest planet, it is a gas planet, so it´s mass is not as great as one might think. As gravity is directly related to mass, it is unlikely that Jupiter´s gravity would have any significant immediate attraction for the Earth due to the vast distances involved.
As the Sun is the centre of the solar system around which all other bodies orbit due to its immense gravity, if it was no longer there, there would not really be a solar system as we know it anymore. The planets would not continue their present orbits and would gradually drift into free space. If they got close to each other, local gravity would have its effect, ultimatley leading to collision.
I think.