Provides a method for increasing the connectivity of I/O resources to a multiplicity of operating systems (OSs) running in different resource partitions of a computer electronic complex (CEC) to obtain sharing of the I/O resources among the OSs of the CEC, including channels, subchannels (devices), and control units (CUs). The invention provides image identifiers (IIDs) for assigning resources to the different OSs. Each shared I/O resource has a sharing set of control blocks (CBs) in which a respective CB is assigned to (and located by) a respective IID of one of the OSs. Each of the CBs in a sharing set provides a different image of the same I/O resource. The different CB images are independently set to different states by I/O operations for the different OSs, so that the OSs can independently share the same I/O resource.