Ow ow ow ow. That is the sound of me, slamming my head onto my desk in frustration, because there is absolutely nothing more painful at ten in the morning then listening to professional wrestling fans talk about business.
The WWE is a publicly owned corporation. There are, for our purposes, two main kinds of stock in this corporation; voting stock and non-voting stock. Within the McMahon family, they hold 70% of the non-voting stock and 96% of the voting stock (as of two years ago, I haven't looked at a corporate guidance since then.) Decisions within the company are made by a Board of Directors, of which Vince McMahon is the chairman. By virtue of controlling most of the voting stock, he usually gets his way within the board, however, it's not full of slouches. Kevin Dunn is amongst the board, as is Lowell Weicker, former Senator and former Governor of Connecticut.
What many people don't understand is that there is a difference between owning a company and operating it. Vince is currently an owner/operator, in that he is heavily involved with business decisions, while being the primary financial backer.
What happens on the business side when Vince passes away? Lawyers would follow the wishes within his will that are legally binding, after the payment of taxes. His assets would be divided up amongst the people whom he listed in his will, in the proportions he set out. If anyone had a 51% share of voting stock or greater, they would be the new "Vince", in that they had enough control over votes in order to guide decisions within the company. If no one had a majority share, then control would fall to the board in general, and major decisions would be taken based on how many voting shares fell on which side. What could easily happen in that situation is a group of people with large voting blocks and common interests (read: Paul, Shane, and Stephanie) could band their votes together to maintain mutual control.
What happens on the creative side? Inside WWE's corporate guidance every year, there's a statement to the effect of "If our Chairman is incapacitated or unable to perform his duties, we have no idea what's going to happen." HHH/Steph have been running creative for some time now, but are they ready to go it alone? You can't guess at that, that's a trial by fire right there. Are the connections that the Levesques have in the entertainment industry as strong as the ones in the McMahon family? Who knows. Creatively, there wouldn't be any immediately noticeable effect, but over the first couple of years there will be some major hiccups as the WWE promotional machine resets itself from the top.
With that being said, if your only experience learning about business and private ownership is watching Dixie Carter get screwed out of her company, please, spare the rest of us the headaches.