In RECENT YEARS an increasing number of law firms across the country have opened Washington offices, but none of Washington's largest firms had branched out into other parts of the country.

Now that trend is starting to change. Wald, Harkrader & Ross, which has tripled in size during the past five years with the help of two mergers, is about to open a branch office in Dallas.

A check of Martindale-Hubbell, the law directory, shows that none of Washington largest firms - those with more than 50 lawyers - has a domestic branch outside this area, although some of them are branches themselves of out-of-town firms.

"We're reversing the flow," said Robert L. Wald, the senior partner of Wald, Harkrader & Ross, which now has almost 60 lawyers in the firm.

"We have a number of Texas clients. We thought it would be interesting to do it the other way," Wald said.

He said that Robert M. Cohan will return to his home town of Dallas to open a branch office of the firm around Jan. 1. Calling the new branch "a modest effort," Wald said he isn't sure if another firm member will move with Cohan or whether a Dallas lawyer will be hired.

Wald said the branch will concentrate on better serving the firm's established Texas clients, not in developing local clients.

Wald said the firm decided to locate a branch in Dallas because only one Dallas firm has opened a Washington office while every big Houston firm has an operation here.

"The street isn't so crowded," said Wald.

The Dallas firm in Washington is one of the biggies - Akin, Gump, Hauer & Feld, the former firm of top Carter advisor Robert Strauss. It has expanded its Washington office during the past five years from eight lawyers to 50.

In case you didn't know, it costs big bucks to take a case to the U.S. Supreme Court.

The final figures aren't in yet, but it looks as if the legal fees in the Bakke case - which led to one of the most important decisions the Supreme Court made this year - will total more than $300,000.

And it looks as if the State of California's university system - that is, the taxpayers - will have to pay Bakke's share as well as its own.

In a reverse discrimination suit, Allan Bakke charged that the University of California Medical School at Davis admitted less qualified minority students under a quota system while rejecting him. The court ordered him admitted while saying some forms of affirmative action programs are constitutional.

Bakke's lawyer, Reynold & Colvin of San Francisco has asked the state supreme court to order the University of California to pay his legal fees either under U.S. civil rights law or a state statute that allows winning attorneys to collect fees from the government in cases where there is a public benefit.

Colvin said he went to California's highest court to get a decision as to whether he is entitled to have the state pay his fees, to save time. If the court says yes, he will apply for a specific amount to the trial court.

He said he has not counted his hours yet, but guessed he should be entitled to about the same amount of money that Donald Reidhaar, the general counsel for the University of California, said he paid to lawyers - which is more than $150,000. This figure does not include the cost of Reidhaar's own time on the case.

The state's main legal fees broke down this way: $51,500 to Paul Mishkin, a professor at the University of California Law School at Berkeley who billed at $100 an hour; $32,600 to Jack Owens, a San Francisco lawyer who billed at $50 an hour, and $44,000 to Harvard Law professor Archibald Cox, who argued the case in the Supreme Court and billed at $115 an hour.

These fees, incidentally, do not include the many thousands of dollars paid 162 groups that filed a record 57 friend-of-the-court briefs with the Supreme Court. Nor do they include the time spent by the federal government - including the Justice Department, the Department of Health, Education and Welfare and the White House - in figuring what the administration's stand on the case should be.

The case brought instant fame to Bakke's lawyer, Colvin, who is dipping his tow into the lecture circuit with a speech Thursday at the U.S. Air Force Academy in Colorado Springs.

"The colleges all want him," said his agent, Cherylyn Davis of Crystal Presentations in Belvidere, Calif., even at a $1,500 to $2,000 fee. But Colvin said he's pretty busy and doesn't know how many other speaking engagements he'll take. "She talked me into this one," he said.

For some young law students, the big bucks start early. First year law students lucky enough to be hired by the top Washington firms were paid $450 a week this summer (that, $23,400 a year). In New York, the top firms paid even more, $500 a week.

The firms figure it's part of the recruiting process; they get a line on the best and the brightest law students who they might want to hire after graduation. For their partner, students are able to do simple legal research.

Short talks: Big crowd expected Wednesday for the Montgomery-Prince George's County Bar Association seminar on Maryland's new divorce law. Luiz R. S. Simmons reports that more than 200 lawyers - about 10 percent of both bars - have signed up and more are expected.