Full Idea
An object a is ontologically independent of b if a can exist without b, if there is a possible world in which in which a exists and b does not. In the strongest sense, an object is independent if it could be all there is.
Gist of Idea
Independent objects can exist apart, and maybe even entirely alone
Source
Peter Simons (Parts [1987], 8.4)
Book Reference
Simons,Peter: 'Parts: a Study in Ontology' [OUP 1987], p.301
A Reaction
Simons calls the strongest version a 'startling' one which maybe not even God could achieve.