SUDDENLY that abandoned real estate child, the 12-building Rockefeller Center, has become a sought-after darling of big-name investors. Japan's Mitsubishi Estate Company Tuesday relinquished its majority ownership of the famous New York property, handing it over to Rockefeller Center Properties Inc. This publicly traded real estate investment trust (REIT) holds a $1.3 billion mortgage on the center. In the morning, the trust reached a $250 million deal with an investment group headed by Chicago real estate magnate Sam Zell. This group includes Merrill Lynch & Co. and Walt Disney Company. General Electric Company, whose NBC television subsidiary is headquartered in the complex, said it will join the Zell group as a 25 percent partner. Hardly had the ink dried when Goldman, Sachs & Co. made a counterbid to pay up to $250 million for an additional stake of as much as 16.5 percent in the trust. Goldman and its investment fund already hold $225 million in the REIT's debt along with warrants and rights to a 19.9 percent stake in the REIT. Now the shareholders of the Rockefeller Center REIT have a choice - both American. Reflecting the more cheerful news, shares of the REIT rose 11 percent, or 75 cents, to $7.875 on the New York Stock Exchange. The two proposals are complex and the REIT and its financial adviser, PaineWebber Group Inc., are expected to take several days to analyze the new offer. There is some speculation that Zell and Goldman could join forces in a deal. Another complexity is that any deal must be approved in bankruptcy-court proceedings - a process that could change the final terms of any settlement Rockefeller Center, the stylistic Art Deco complex built in the early 1930s by John D. Rockefeller, was sold by the Rockefeller family to Mitsubishi Estate Company of Japan in 1989. Mitsubishi's total investment reached close to $2 billion. Mitsubishi gained an 80 percent ownership stake, the Rockefeller family a 20 percent share. But sagging real estate values, coupled with high vacancy rates in the early 1990s, prevented Mitsubishi from turning a profit. On May 11, Mitsubishi sought bankruptcy protection for the complex. Zell already controls 29 million square feet of office space around the US. Rockefeller Center contains an additional 6 million square feet. Among Zell's more prominent holdings, says a spokeswoman in Chicago, are the Chicago Title and Trust Company building, a relatively new structure in downtown Chicago; and a 1.4 million square foot office complex in San Francisco. Rockefeller Center would be his most prominent acquisition. ''But how many more prominent real estate holdings are there in the United States?'' asks Zell's spokeswoman. What will happen to the Rockefeller complex is now the big question here. Currently, it is operated as a whole. That organizational structure has protected the center's park-like ''open spaces.'' Rents reportedly run around $30 a square foot. Most leases are long-term. That makes it difficult for new owners to quickly boost leases toward the levels of $35 per square foot and up found in mid-town Manhattan. One possible solution, say experts, is that the new owner might be persuaded to sell off parts of the complex, turning some buildings into business-related condominiums. ''Typically, a premium is paid by owner-users,'' says William Kinn, a senior vice president of Landauer Associates, New York real estate consultants.