When Robert E. Allen, a thoughtful business executive with a soothing voice and penetrating gaze, first heard a deal had been struck, his head started to swim. Then he was hit by a spell of insomnia.

For a man who had spent his entire career in the Bell Telephone System, the agreement to break up the world's biggest corporation was a jolt. Only four months earlier, Allen had moved a notch up the corporate ladder to become president of the Chesapeake & Potomac Telephone Companies, a $6.9 billion Bell operating group that is the Washington area's largest private employer.

Now, along with other senior Bell executives, Allen, 47, was finding out three days before the rest of the world that American Telephone & Telegraph Co. would be split apart.

"I didn't sleep for two nights just thinking about all the implications of such a change," Allen recalls. "All of our heads were spinning." He was kept awake thinking about what lay ahead: his employes' fears, customers' doubts, how to unscramble some highly complex financial and technical puzzles. "You think about separating the assets . . . . You just ran the whole gamut."

How C&P confronts these uncertainties may have a sizable impact in the Washington region. The four C&P companies employ 45,000 workers, including 15,000 in the metropolitan area--more than any other employer here except the U.S. and local governments. C&P's telephone lines are connected to more than 4 million homes and businesses in the District of Columbia, Maryland, Virginia and West Virginia.

C&P, complaining of an earnings squeeze, is already pressing for steep increases in phone rates and a new way of charging for local service: "measured" rates, based on the time of day, distance and duration of a call. And C&P plans to spend a record $1 billion this year on new facilities, including a new regional C&P headquarters near Silver Spring.

As the company prepares for its 100th anniversary next year, some regulatory officials, investment analysts and labor union leaders--along with some of C&P's own employes--see little cause for celebration.

"Will C&P have the same things in the future? Are they going to be like a struggling company? Are our pension benefits going to be the same now?" asks Harsh Barger, an information operator who has put in nearly 22 years at C&P. "I'm very concerned."

But Allen, his initial dizziness long since worn off, now looks ahead eagerly. "We are going to be more in control of our destiny, and we will have a clearer mission. And I think there are exciting days ahead."

Whether the AT&T breakup will bring about significant increases in local telephone rates is a complex issue, tangled in political controversy and regulatory debate. Moreover, C&P proposed its latest rate increases before the antitrust agreement was announced.

"The bottom line is that people ought to pay for what they use," Allen says. "If we're stimulating telephone usage that just causes our cost to go up but not our revenues, then we've got a problem." The proposal for the new "measured" payment method, similar to those established for long-distance calls, has drawn opposition from consumer advocates, groups representing the elderly and the communications' workers union. Some critics assert the plan amounts to putting a pay phone in every customer's home.

The Jan. 8 antitrust settlement, still undergoing court review, would require AT&T to give up the four C&P companies along with 18 other regional operating subsidiaries. The newly independent operating firms would offer basic local phone service. AT&T would hang onto its long-distance business. It would also sell telephones and other equipment produced by its Western Electric Co. subsidiary and continue its Bell Laboratories research work.

How C&P will emerge from the divestiture proceedings is not yet certain. It is expected to lose nearly half of its employes to the split-off AT&T enterprise, including those who deal with long-distance service and terminal equipment, like home phones and business switchboards.

Under a "planning model" proposed yesterday by AT&T, the four C&P companies would be grouped with the Delaware, New Jersey and Pennsylvania phone systems to form one of seven regional enterprises. Nevertheless, the announcement said the present companies would remain separate and "retain their own identities."

Analysts, including Page Montgomery, vice president of Economics and Technology Inc., previously suggested such a setup was likely. They cited AT&T's move last year to establish six marketing regions for its new equipment subsidiary, known as "Baby Bell." This also grouped C&P with the Delaware, New Jersey and Pennsylvania systems. A regional company formed solely of the four C&Ps still remains another option, some analysts note. This arrangement, Allen says, would make C&P a "model structure" for the rest of the Bell System.

Shortly before the plan to break up AT&T was announced, C&P had taken steps to impose more centralized control over its widely scattered operations. Nevertheless, it remains a corporate hybrid: four distinct companies in the District and three states, all linked to C&P's central headquarters and run by a single president, Allen. He attends meetings of four C&P boards of directors. C&P officials attribute their unusual setup partly to state laws that, they say, required separate Maryland and Virginia charters.

While the antitrust agreement restricts the business activities of local phone companies, C&P officials point to several possible ventures. One is "cellular" radio, a new form of mobile communication for use in automobiles and eventually in homes and offices. C&P may some day also invest more heavily in supplying cable hookups and other transmission facilities to cable television broadcasters, executives say.

Nevertheless, investment analysts expect little sparkle in C&P's future. "You're going to have an unattractive utility-type business which is dependable and very dependent on regulatory approval of rate increases ," says Eliot H. Benson, vice president and research director of Ferris & Co. Inc., a Washington investment firm. "They might grow at 3 or 4 percent a year, which is the rate that the average utility grows at," says Ernie Kiehne, research director of the Baltimore-based Legg Mason Wood Walker Inc. "It's a good return for an older person or a conservative person."

The Bell split-up may discourage C&P investors for another reason. "One of the greatest appeals of big telephone over the years has been its diversity of regulatory involvement," says Louis Hannen, senior vice president and research director of Wheat, First Securities Inc. in Richmond. Stringent regulation and lower earnings by a phone company in one part of the United States, he notes, may be balanced by higher earnings and less harsh regulation in another.

Regulatory officials and telecommunications researchers have expressed widespread concern about the future of the local operating companies, including C&P. They worry that local phone rates may rise and that technological advances may some day make local phone systems entirely or partly obsolete. If so, a preliminary staff report by the Federal Communications Commission said, the antitrust agreement, which limits the operating companies' business activities, may itself become "an unnecessary barrier to competition."

Although C&P executives say most employes have recovered from their initial dismay at the divestiture announcement, labor union officials and some employes express doubts. "It's going to be more difficult to get the same wage scales out of the local companies than it will out of AT&T," says George Strick, a Communications Workers of America vice president who oversees union relations with C&P. "You're just not going to have a lot of growth in the local companies." The AFL-CIO union bargains over wages and benefits for about 33,000 C&P employes.

Uncertainties trouble C&P workers. "I'm glad my future's behind me," says Lois Carroll, 60, a long-distance operator who has spent 30 years at C&P. "It's bound to bring changes and they are not going to be changes that we are all going to like." Says Paul Barr, 26, a long-distance C&P operator for 3 1/2 years: "It's going to prohibit a lot of career moves for a lot of younger employes. It's going to hurt me in that regard."

Over the years, the Bell System has given employes a feeling of security, a sense of belonging to a harmonious corporate family. For some, this emotional tie was snapped by the antitrust agreement. "I have the best job in the phone company. I'm very happy," says a highly skilled electronics technician with 18 years at C&P. But he asks, "What's C&P going to be left with? . . . We're going to be a very small company."

Critics have compared the local phone companies to declining railroads and financially troubled power companies. To Allen, such talk amounts to unjustified pessimism. "I think that's a bad rap. I think that's a bad comparison," he says. "If our services are properly priced, we're in the catbird seat."