Speculation is mounting that Samsung could be shaken up after the death of chairman Lee Kun-hee.
Shares in several Samsung businesses rose amid reports that his heirs could be forced into asset sales or dividend payments in order to pay a massive inheritance tax bill.
Mr Lee, who helped to build Samsung into Korea's largest conglomerate, died over the weekend aged 78.
Analysts say his heirs face billions in taxes from his share assets alone.
That includes his scandal-struck 52-year-old son, Lee Jae-yong, who has managed the sprawling South Korean technology group since 2014.
Lee Jae-yong has twice been accused of fraud over his role in a 2015 merger deal at the tech giant and is currently awaiting trial.
At 50%, Korea's inheritance tax rate is one of the world's highest. A premium can be added to shares if the deceased has a controlling interest in a company, potentially taking the top rate to around 60%.
By comparison, inheritances are taxed at 40% in the UK, and although the top rate is similar in the US, the minimum threshold is set so high that few Americans actually pay it.
Mr Lee was the richest person in South Korea, according to Forbes, with a net worth of nearly $21bn (£16bn).
He took over Samsung in 1987, and introduced radical measures which helped propel the company from a second-tier electronics manufacturer to an international tech giant.
He owned major stakes in the conglomerate's crown jewel Samsung electronics, as well as the holding company Samsung C&T, Samsung Life Insurance and Samsung SDS.
Mr Lee is survived by his wife, Hong Ra-hee, his son Lee Jae-yong and his two daughters, Lee Boo-jin and Lee Seo-hyun.
Each is already a billionaire in their own right, according to Forbes.
"The inheritance tax is outrageous, so family members might have no choice but to sell stakes in some non-core firms," NH Investment Securities analyst Kim Dong-yang told Reuters.
Any shake-up of the conglomerate, however, could depend on what the firm's de facto boss Lee Jae-yong chooses to do.
Alternatively, Samsung's affiliates might also pay higher dividends, leaving more money for the younger generation of Lees to pay the bill.
Speculation over the future of Samsung following Mr Lee's death has stirred investor interest over various units of the conglomerate.
On Monday, shares in Samsung C & T surged by 21.2%, while Samsung Life Insurance rose 15.7%.
Shares in Samsung Biologics, Samsung SDS and Samsung Engineering also tracked higher.