The state will own the right of way and lease it out to the Cintra-Zachry consortium, which will put up the money to build the road and maintain it, while collecting tolls to make up for the expense and get some profit as well, for a term of 50 years. The state will own the road; Cintra-Zachry will merely build and run it.
I forgot to mention that Cintra-Zachry will put up a huge concession fee to the state of Texas just to build and run the road.