[filmackay]

A spin-off (or more correctly, demerger) is almost exactly what you describe: a company cloning itself but adopting a different vision/mission, and awarding shares to all existing shareholders.

With companies it is usually done with a particular division, or business area - but in the case of an anti-trust settlement (go and compete with yourself) it would be exactly what you describe and be implemented as a demerger.

[the_mitsuhiko]

Except even people not owning shares in the company can split it.