-- After months of intense public scrutiny, the family that controls Cablevision Systems Corp. is offering to take the cable TV provider private, marking the latest dramatic turn for a company that has been split by a family feud and mounted a fierce showdown with the mayor of New York.

At the same time, Cablevision would spin off its Rainbow Media Holdings LLC subsidiary, which holds lucrative cable channels -- AMC, the Independent Film Channel (IFC) and WE: Women's Entertainment -- and several regional sports networks, Madison Square Garden, and the sports teams that play there, the New York Knicks and the New York Rangers.

Cablevision chief executive James L. Dolan, who had sided with board members in opposing a satellite venture championed by his father, Charles, the chairman, would head up the Rainbow unit to be spun off while remaining a director of Cablevision. Charles would continue as chairman of Cablevision.

The Dolan family, which controls the company through a special class of supervoting shares, announced the proposed transaction Monday. Under the terms of the deal, Cablevision shareholders would receive $21 per share in cash as well as stock in Rainbow estimated to be worth $12.50 per share.

The combined value of $33.50 per share, or $7.9 billion, represents a 25 percent premium over the closing value of Cablevision's shares Friday. Cablevision's shares jumped $5.13, or 19 percent, to close at $32 Monday on the New York Stock Exchange.

The Dolans said in a statement that they were interested in only the going-private transaction and did not plan to sell their stake to another party. They said a committee of independent directors on the company's board would review the proposal on behalf of the company's public shareholders.

Cablevision's 3 million cable customers, clustered around the New York area, as well as an industry-leading rollout of premium services such as digital phone and high-speed Internet, make Cablevision an attractive takeover target.

The Dolan family, through a spokesman, declined to make any comment on the transaction beyond their statement. A Cablevision spokesman also declined to comment.

If the deal goes through, Cablevision would become the second major cable TV company to go private in recent months. In October, Cox Enterprises Inc., a privately held media conglomerate based in Atlanta, bought out the public shareholders in its cable TV unit, Cox Communications Inc.

This spring, the company was divided over whether to pursue an expensive venture into satellite broadcasting. Charles Dolan championed the venture, called Voom, while James sided with board members who wanted to shut it down. The business eventually closed down but still operates several high-definition cable channels.

Cablevision also sued to block the development of a stadium and convention center in Manhattan, which would have competed with Madison Square Garden. The company mounted a bitter campaign against New York Mayor Michael R. Bloomberg after its bid to develop the land was rejected.

Charles F. Dolan, shown in this 1997 photo, would remain Cablevision chairman if the company is taken private.