Warren Buffett's birthday this week was good news for Berkshire Hathaway investors who could celebrate another year of the Oracle of Omaha's leadership. But the milestone also reminded shareholders they need to think about who will run the evolving company after Buffett is gone.

The more than 80 businesses that Buffett has accumulated at Berkshire (BRK.B) are mostly coasting along well, posting a profit of more than $3 billion in the most-recent quarter. Its Class A stock (BRK.A) closed at $126,559.90 a share on Friday - less than $2,500 away from its 52-week high set in early August and $27,608 above the 52-week low.

So there's plenty for shareholders to celebrate.

But Buffett's advancing age - he turned 82 on Thursday - coupled with his radiation treatment for prostate cancer this summer, keeps his mortality on the minds of many Berkshire investors. Buffett has said the cancer isn't life-threatening, and he is feeling good.

Buffett has outlined Berkshire's succession plan and reassured investors that his board has chosen a successor and two backup candidates, although he won't say who the company's next CEO will be. Buffett is both chairman and CEO.

Buffett has no plans to step down, saying he enjoys the deal-making too much, even though he hasn't landed a sizable acquisition since buying chemical maker Lubrizol for $9 billion last year.

Whoever takes over Berkshire after Buffett will inherit a sprawling conglomerate that is evolving with each new acquisition. The Omaha-based company now relies less on the insurance companies and investments it has long been known for and more on its railroad, utility and manufacturing companies.

"The insurance is increasingly more of an engine that runs in the background instead of the driver of the business," said Jeff Matthews, an investor who wrote Secrets in Plain Sight: Business & Investing Secrets of Warren Buffett.