Blackwater indeed.

"In a corporatist economy such as ours, government funnels lots of money to nominally private firms to accomplish things it might have done directly. But there is no essential difference between those two ways of doing things. What counts is who controls the money.

If the government were to close down the Internal Revenue Service and hire H&R Block to collect taxes, would that be privatization of the tax system? The question answers itself."

- Sheldon Richman

In fact, I'd say that the pure government situation is more desirable in some ways, because there's no particular motivation for malfeasance. And to paraphrase Murray Rothbard, it's better for criminal actions to be as inefficient as possible.
Unfortunately there's no other concise term for this sort of government-business partnership than Fascism, which has been historically tainted.
Tainted or not though, it's the most accurate term for this that there is.