* Cho died in U.S. hospital after chronic illness - airline
* Holding co shares up over takeover battle expectations -analysts
* Cho's family to pay inheritance taxes for his shares - analysts
* Cho family plagued by scandal after "nut rage" incident (Updates with inheritance taxes and comment from nut rage whistle-blower)
By Ju-min Park and Heekyong Yang
SEOUL, April 8 (Reuters) - Korean Air patriarch, chairman and CEO Cho Yang-ho died of a chronic illness on Monday, weeks after shareholders ended his 27-year tenure on the board of the country's biggest carrier due to perceived leadership failings.
Shares of the family-controlled airline and its parent Hanjin Kal Corp jumped on hopes of better governance under new management following Cho's death.
Analysts say the death raises the possibility of a bidding war over the 70-year-old patriarch's stake in Hanjin Kal, but his family would fight to defend control of the airline.
"Of course, his family will try to inherit his shares, but that can take time and money ... that opens a window for expectations about a takeover battle," said Um Kyung-a, a Shinyoung Securities analyst.
Inheritance tax the family needs to pay may amount to around 170 billion won ($148 million), worth half the entire Hanjin stake held by Cho, some analysts estimate.
Cho holds a 17.8 percent stake in Hanjin Kal. Cho, his relatives and the family's academic foundations own a total 29 percent of the holding firm. Cho's only son, company President Cho Won-tae, is widely seen as his successor.
A South Korean activist fund is the No.2 shareholder after the Cho family and recently boosted its stake to 13.5 percent, vowing to take a role in management to fix poor governance.
Korean Air has been plagued by scandals involving founding family members, culminating in the indictment of Cho in 2018 on charges of embezzlement and breach of trust.
Cho denied the charges.
The troubles began after Cho's eldest daughter, Heather Cho, made headlines in 2014 when she lost her temper over the way she had been served nuts in first class and ordered the Korean Air plane to return to its gate at a New York airport.
The "nut rage" incident tarnished the carrier's image, while subsequent scandals involving Cho's daughters only deepened concerns around the family's leadership.
Shareholders forced Cho off the board in a landmark vote on March 27, making him the first founding family member of any South Korean corporate giant to be ousted in such a manner.
The vote added momentum to growing shareholder activism in Asia's No.4 economy, long dominated by family-run business empires accused of ignoring minority investors.
After the announcement of Cho's death, Hanjin Kal jumped almost 25 percent to a more than two-month high, while the broader market was flat. Korean Air ended 1.9 percent higher.
Before his family's high-handedness became an object of public ridicule, Cho was known for his business acumen.
He gained a reputation for daring and smarts as he built the airline into one of Asia's biggest, operating 166 planes with international flights to 111 cities in 43 countries.
He died from a chronic ailment in a Los Angeles hospital early on Monday Korean time. A company official said Cho had surgery for lung disease a while ago and his condition had worsened over the past two years.
His death, however, came as a surprise as his condition was not publicly known. Only last year, he had carried the torch for the Pyeongchang Winter Olympics.
His name was the most-searched keyword on South Korea's top internet portal on Monday.
Korean Air in a statement paid tribute to Cho's enthusiasm, but conceded "not everything went well", a reference to the shareholders' vote to unseat him from the board.
"Taking his passing as an opportunity, the family should change the way they have managed the company and employees in a fair and unforced way," said Park Chang-jin, a Korean Air flight attendant who disclosed the "nut rage" case in 2014. ($1 = 1,144.4200 won) (Reporting by Ju-min Park, Heekyong Yang and Joori Roh; Editing by Stephen Coates and Himani Sarkar)