Cablevision Systems’ controlling Dolan family has presented a proposal to take the No. 6 cable operator private in a $7.9 billion deal that would involve spinning the noncable system assets into a public company.

The proposal comes as a growing number of cable operators look to exit the public markets, which have penalized cable companies amid stiffening competition from satellite, the emergence of large telephone companies as competitors and worry that cable has little growth opportunities ahead of it. Cox Communications went private late last year, and now Insight Communications is in the process of doing the same.

The move also comes as Cablevision’s internal strife among family members has played itself out in very public way. Cablevision Chairman Charles Dolan and his son, CEO James Dolan, were locked in a pitched battle this past spring over whether or not to fund the ill-fated Voom satellite service, which has since been shut down.

Under the proposal that the Dolans made to the Cablevision board Sunday, the family, which owns 20 percent of the company’s stock but through certain rights has 71 percent voting control, will pay an estimated $33.50 a share, or a total of $7.9 billion, for all outstanding Cablevision shares. The price represents a 25 percent premium over last Friday’s closing stock price.

The company’s cable and telecom assets would make up the new Cablevision, which would have Charles Dolan as chairman and Tom Rutledge as CEO. Mr. Rutledge is presently chief operating officer of Cablevision.

The remaining assets would become part of a publicly traded company to be known as Rainbow Media Holdings, which would be led by James Dolan as CEO. The assets included in the new Rainbow will include cable channels AMC, IFC and WE: Women’s Entertainment; music channel Fuse; regional sports networks; Madison Square Garden; professional sports teams the New York Knicks and New York Rangers; Radio City Music Hall; News 12; and Clearview Cinemas.

Though some analysts have suggested that Cablevision’s privatization offer might spur others to make competing bids for the company’s value cable systems, the company has said that it will not entertain external offers.