The expected breakup of American Telephone & Telegraph Co., ordered in an antitrust settlement last week with the Justice Department, has caused an immediate controversy about whether local rates will increase sharply as a result.

AT&T Chairman Charles L. Brown and Assistant Attorney General William F. Baxter both say increases would occur -- but at the same rate that would have taken place without divestiture.

Yet heads of several Bell System operating companies and many economists say otherwise. Just what is going to happen to phone bills? Following are questions and answers on this issue:

Question: Does the settlement AT&T signed last week mean an immediate increase in telephone rates?

Answer: No. If there are any rate changes as a result of the settlement, they are probably one and a half years away. Under the AT&T-Justice Department agreement, the Bell System has 18 months to divest itself of the local operations of its 22 local operating companies. AT&T has the option of creating one new nationwide company for all local service, several regional companies or separate local firms for the 22 current subsidiaries, including Chesapeake & Potomac Telephone of D.C., Maryland, Virginia and West Virginia.

Any local rate increase would have to be approved by state and District of Columbia regulatory agencies, a process which normally takes several months to a year. Even before the settlement was announced, Bell System companies had dozens of requests for rate hikes pending before most regulatory agencies in the United States.

Q: Will rates still be regulated when the divestiture plan does take effect?

A: Yes. State and D.C. public service commissions still will regulate local rates. Long-distance rates will be regulated by the Federal Communications Commission, at least for the next few years.

Q: If rates continue to be regulated, why won't they stay down?

The job of the regulators is not to keep rates down, but to keep rates fair -- for both consumers and the stockholder-owned telephone companies. Regulators have been approving steeper rate increases over the past few years because of higher costs and changes in federal policies designed to link rates more closely to costs. These factors guaranteed future rate increases even before the settlement.

C&P here recently asked the D.C. Public Service Commission for its biggest rate increases ever -- including a 72 percent rise in the most commonly used local residential service. C&P also has asked for a 28 percent boost in West Virginia and a 26 percent increase in Maryland. A 10 percent surcharge was imposed on Virginia phone bills in November.

Q: Why the steep increases?

A: Within the past year, AT&T has begun a nationwide effort to raise local phone bills, saying they were priced below costs. AT&T long has maintained that long-distance rates have been priced higher than costs to subsidize local rates.

To meet the increasing long-distance competition from such firms as MCI Communications Corp. and Southern Pacific Communications Corp., AT&T argued it had to redesign its rates to make local use shoulder a larger share of the costs.

Some of AT&T's competitors disagree. They say some local rates, especially those in large metropolitan areas, are set higher than costs to help subsidize AT&T's activities where it faces competition.

Q: Won't the absence of subsidy mean even higher local rates then?

A: Possibly, but not necessarily. If AT&T is correct, divested local firms no longer will be able to subsidize local service with long-distance revenues. That may leave local companies no choice but to boost rates more than they would have. But your long-distance bill may go down. Faced with increased competition in the long-distance area, AT&T probably will want to strive to keep long-distance rates down.

There may be other ways to use long-distance revenues to subsidize local calls and keep rates down. For instance, a whole new rate structure will have to be set up in which long-distance companies will have to pay a fee to obtain access to the local company's network and, ultimately, the end user. In Congress, some key legislators are discussing legislation that would guarantee a rate structure to support lower local bills.

Q: How many bills will I get?

A: This is unclear. Some suggest you may get at least two bills, one for local service and additional invoices for each long-distance company you use. Others say these charges may be included in a single bill through an arrangement between local and long-distance firms.

Q: What will happen to pay phones?

A: They will be owned by AT&T, not by a local phone company, but rates for pay phone calls apparently still will be regulated by state utility commissions.

Q: What about purchasing phone equipment?

A: As now, equipment will be available at stores run by competiting companies, including AT&T.

Q: What about phone directories and Yellow Pages?

A: The white-page directories will be published by local phone companies. But the Yellow Pages will become the responsibility of AT&T and competitors.

Q: What about dialing 411 or long-distance information?

A: Local phone companies still will provide 411 service at rates regulated by state and D.C. regulatory commissions. It is unclear whether there will be special charges for long-distance information calls.

Q: Is there anyone I can complain to if I don't like what seems to be happening?

A: It depends on the nature of your complaint or question. U.S. District Court Judge Harold H. Greene, who still is considering the divestiture issues, may allow a period for public comment. The Maryland and D.C. Public Service Commissions and the Virginia State Corporation Commission normally allow public comments on rate proceedings. So does the Federal Communications Commission. Congress is considering possible telecommunications legislation, and opponents of the AT&T divestiture plan already are urging citizens to contact their senators and representatives. Some also suggest writing to the Justice Department's Antitrust Division.