"complete ownership" is correct and usable in written English.
You can use it to describe the total control someone has over something, for example "He had complete ownership of the business."
I never felt I had complete ownership over Bond.
But the new contract gives the league complete ownership.
"He has taken complete ownership of his golf swing and he understands it more than most.
"That thing at the Marquis I feel complete ownership of," he said.
When HSBC bought Republic National, Browder embarked on a series of share deals which has left him with complete ownership.
Under federal law, the government has "complete ownership, possession and control" of presidential and vice-presidential records.
As it turns out, Digeo did not have the complete ownership of the patent that it thought it had.
He now has complete ownership of his game and, with his unwavering self-belief, his natural talent has shone through".
He arranged distribution through Columbia Records, taking no advance payment but retaining complete ownership of the album.
The Yankees fell to 10th and last place, and during the season CBS took over complete ownership.
More acquisitions followed over the years, and in 1955 South Penn Oil acquired complete ownership of Pennzoil.
