Earlier in the year, Donald Trump Jr. was asked under oath if there is a specific entity owned by his father that he works for.

“I’m sure there is,” he said in a court deposition. “I don’t know exactly what it is.”

In recent years, Donald Trump Jr. and his siblings, Eric and Ivanka, have taken on increased roles and been empowered by their father to make more decisions for the complex amalgamation of hundreds of businesses that comprise the Trump Organization. Even so, they continued to go to their father for counsel and affirmation in their decisions, and the elder Mr. Trump ran the businesses with a heavy hand, interviews and court records show.

Now that practice will be tested. The President-elect has been pushed by ethics experts and others to fully divorce himself from his businesses due to numerous potential conflicts of interest. He recently postponed a news conference in which he was to explain his plans, with his spokeswoman saying his advisers needed more time to reconfigure a business structure that is “convoluted and complex.” He has said he won’t be involved in his business while he is president, and tweeted on Tuesday morning that his sons would run the business and that it wouldn’t engage in new deals.

Ethics experts said that although details are slim and not taking on new deals may avoid some conflicts, that arrangement seems likely to still be problematic since Mr. Trump could make decisions as president that affect his financial interests. Another issue is that the company probably would do day-to-day transactions such as leasing space and dealing with banks that could involve partners whose interests overlap with the government, they said.

The Trump transition didn’t respond to requests for comments on those concerns or about the children’s role in the company.

Some former employees and business partners say it will be difficult for Mr. Trump to fully stay away—or the children to stay away from him. “All decision making was made by Mr. Trump and signed off by Mr. Trump in writing, period, across the board,” said Michael Boccio, a former attorney at the company who left in 2011.

One sign of Mr. Trump’s hold over the company is the extent to which he has kept full ownership of his assets despite his children’s employment at his companies. The financial disclosure form he filed earlier this year as a requirement of running for president lists “Trump family members” as part owners of only 32 of the over 500 assets listed.

In some ways Mr. Trump has long been acting as if he was planning for his children to take over his companies. They worked odd jobs, such as landscaping, at his businesses growing up and came to work for the company in more-senior roles as young adults. Eventually their father gave them increasing responsibilities.

One example of that was in 2007 when the Trump Organization created a Trump hotel brand with heavy involvement from his three grown children with plans to do marketing, branding and management deals throughout the world.

In his deposition involving a business dispute over the redevelopment of the old Post Office building in Washington into a hotel, Donald Trump Jr. said the hotel company is “more my siblings’ baby than it is his” father’s, and that his father is mostly involved in large equity deals.

From Trump Tower offices next to one another, each of the adult children runs his or her own teams of employees that oversee specific projects, according to former employees and court records.

They each have the same business title—executive vice president of development and acquisitions—but that hardly describes the way they divided up various duties.

Eric Trump took on a winery project in Virginia and golf course acquisitions and construction, and has overseen the Las Vegas hotel.  Ivanka Trump has been heavily involved in the hotel development business, particularly the redevelopment of the Post Office building. Donald Trump Jr. has embarked on many of the company’s offshore licensing deals as well as domestic commercial leasing deals, according to court records, company statements and former employees.

In recent years, as Donald Trump has veered further into politics, the children have taken on larger roles at the company, including bringing new deals and carrying them out. Foreign developers building Trump-branded projects say they have dealt almost exclusively with the children during this time.

“As a matter of fact in the last couple of years we did not bother [Mr. Trump] with any details,” said Hussain Sajwani, who is building two Trump-branded golf courses in Dubai. Mr. Sajwani said he dealt primarily with Ivanka and Eric Trump.

Still, the children have continued to seek out their father’s input at critical junctures. Ivanka Trump said in a sworn deposition earlier this year that at one point, after Mr. Trump began running for president, two celebrity chefs pulled out of a planned restaurant at the Washington hotel.

Ms. Trump, who was spearheading the project, said she went to her father to ask what they should do with the empty space. It was a practice so common, she said, she couldn’t remember when or where it would have occurred.

“I would have definitely asked his opinion,” Ms. Trump said in the deposition. “We talk at dinner, we talk on the telephone we talk at—so I don’t know when I—I would have brought to his attention our thought process around that highly visible component of the building.”

The family hasn’t indicated what role Ms. Trump will have in the reconfigured company, if any.

The business ventures involving Mr. Trump’s children have had mixed performances.

For example, the Trump Hotel Collection in 2007 had 12 projects in development. Some of them opened successfully, like the Trump International Hotel Waikiki Beach and the Trump International Hotel Las Vegas.

But others, including projects in Cap Cana, Dominican Republic, and New Orleans, never got off the ground. Projects in Baja Mexico and Fort Lauderdale ran into controversies and lawsuits partly because of the financial crash that hit shortly after the Trump Hotel Collection was launched. More recently, the Toronto hotel and condo tower, which opened in 2012, has gone into receivership amid poor sales and legal disputes.

Yet the Trumps and family friends have said recently that Donald Trump has more trust in his children than he had in the past.

“Those three children don’t need a nanny,” Richard LeFrak, a friend of the family who presides over another New York real estate dynasty, said in an interview last week.

Write to Alexandra Berzon at alexandra.berzon@wsj.com and Peter Grant at peter.grant@wsj.com