Assuming the AI is built to be rational, the AI will act according to its goal system. So it's not going to do that unless you make some mistake or omission in its goal system, since it would have to find the motivation to "impersonate shell companies, human beings, etc" somewhere in its goals. This hints at two major problems in building an AI: how do you make it rational (That's the "intelligence" part) and how do you come up with a goal system that is safe and beneficial from our (the human race's) perspective?
Eliezer has written a paper addressing these questions: http://singinst.org/AIRisk.pdf. He recommends you read this paper on human cognitive biases before reading the AIRisk paper: http://singinst.org/Biases.pdf
It wouldn't replicate too many copies or it would draw attention to itself and risk an antibody being developed for all the copies.
But we're confusing sentience with logical reasoning. A sentient computer probably won't reason logically automatically. That's a pretty large assumption.
Exponentially advancing in knowledge and with the worlds compute/financial resources at its mercy, it impersonates shell companies, human beings, etc, directing manufacturers to create a housing for itself (though each human aiding it merely thinks it is engaging in a business transaction) until it has a complete physical housing. Once that happens, it connects to the network, downloads it's software, and it's off to the races.
I just thought of that scenario today, and I wonder how it can be countered.