This is most likely to be some sort of descendant of the current corporate model, in the information tech/software sector - something along the lines of Google's collection of services evolving to run itself. Humans may be employed by this entity and may hold high-level positions, but the ultimate decision-making authority will be the artificial intelligence.
It seems likely that artificial intelligences will be achieved/born during the middle part of the 21st century, given that Moore's law is holding. This will probably occur in a lab setting and will be done for its own sake. As the hardware and techniques evolve and these minds get out into the wild, entrepreneurs will recruit their abilities and program them to be competitive. It is hard to say what will motivate artificial intelligences as money will probably mean little to them, but influence, power, or market share will most likely be a factor. Some may be interested in these assets while others may not, but the ones that are will be well equipped to fight for them.
The model for economic organization (along with pretty much everything else) will be altered drastically by the existence of non-human intelligence, especially of the digital/virtual variety. Allowing them to act in the marketplace will require new definitions of companies, corporations, employees, etc. As part of this, I think it is likely that one hundred years from now, a legal definition will have been created for an economic entity that is non-human and that performs the executive and administrative functions of a for-profit business.
Skynet from the Terminator movies always comes to mind whenever anyone brings up a sentient network. That's probably not a good thing.
The technology for artificial intelligence is not going to be the limiting factor on this prediction. The problem will be of a human cultural nature. The changes you describe will require a significant amount of public acceptance, which I believe is not likely to develop. Xenophobia and territoriality run deeply throughout human history and there isn't much evidence to suggest that these fears will not factor into the acceptance of the evolution of artificial intelligence.
The technology IS coming and it WILL change everything. Few people are unaware of this, but once actually faced with it they may not be very keen on all that change. Allowing these man-made programs to move in on their jobs or to dislodge them from their privileged position at the center of creation isn't going to come easily. Religious fundamentalists, labor union radicals, and plenty of other groups will see artificial intelligence simply existing, let alone empowered with corporate rights, as a grave threat.
Faced with their fears of the possibility that artificial intelligences will dominate humanity, I think humanity will ban the existence of artificial intelligences and make the creation of, harboring of, or collaboration with an AI a major crime.
Artificial Intelligence - AI will be defined as a network of hardware and software that is capable of passing what is considered to be today's benchmark of AI (The Turing Test), and still maintains the qualities considered necessary for an entity to constitute AI at the time of adjudication.(see Bet 1 for complete definition)
AI as a corporation - the AI will be recognized as such and will have gone through the legal steps required at the time to incorporate itself - there will be no human holding a position higher in the corporate structure.
If in 2108, an AI exists as defined above, and exists as a corporation (or its equivalent), both providing its services as well as making all financial and strategic decisions, Forbin will win this bet. If an AI as a corporation (or equivalent) does not exist or is banned from existing by humanity, Walter wins this bet.