The federal government now hands out so much money to states and localities that a whole new subdivision of the lobbying industry has sprung up here to fight for it.

Everyone from New York City to the Westlands (California) Water District has representatives here, and a subsidiary of the National League of Cities and the U.S. Conference of Mayors even "rents" lobbyists to municipalities that don't have their own.

The reason isn't hard to spot: federal grants totaling $85 billion a year are available to states and localities, according to the federal budget.

And the results can be spectacular. Rep. Charles B. Rangel (D.N.Y.) credits a $22,000-a-year New York City Welfare Department lobbyist, Liz Robbins, with being instrumental in winning a legislative battle early this year to let New York keep $650 million in federal welfare payments that it otherwise would have had to repay to the government.

No one would argue that Robbins got the provision through herself. Rangel and Sen. Daniel Patrick Moynihan (D. N.Y.) clearly did the major work. But she played a significant role. "No question about it," said Rangel."She helped get the votes."

Thus government entities of all sizes are finding it a very good investment to hire someone to help them get what they can. In addition to working to shape legislation in a manner helpful to their employers, lobbyists also press for favorable distribution formulas for existing programs, they locate possible grants, contracts and research projects, and they keep an eye out for regulations that migh affect their local governments.

Bob Horn, 34, heads the lobbying office maintained by the governor of Michigan in a cozy five-room suite at 444 North Capitol St., a building called the Hall of the States because a big cluster of state governors' representatives are housed there.

Horn is chairman of an organization of governors' representatives here, and he said about 30 states now have official lobbying organizations. But he estimated that if you add up all the cities, states, legislatures, transportation departments, education departments and other local government units that maintain full-time lobbyists. "All told, I'd guess there are several hundred jurisdictions represented." This includes 75 to 80 cities, a couple dozen counties.

Horn said the key to the successful operation is effective liaison between the state governor and the congressional delegation, where the real capitol clout lies.

"Without the congressional delegation we could stand on our heads and spit nickels, we wouldn't get a thing done ourselves."

As an illustration, Horn said a few years ago Michigan was seeking federal money to help in construction of a transit system in Detroit. "We worked very hard with the whole delegation," most of whom in turn worked hard to push the administration for the money -- and they got $600 million from the Ford administration in its closing days.

In another case, Horn's office worked to help Dow Chemical get a $14 million contract for research on low-grade coal shales in Midland, Mich. -- enlisting the support of the congressional delegation and making representations to government agencies on the worth of the project.

The State of Michigan, as one of the nation's largest, maintains lots of public lobbying operations here. Aside from Horn and associates Peggy Monihan and Shannon Campbell, the Michigan departments of education and commerce each have a lobbyist swinging in from the state three to four days a week, working out of Horn's suite. The Michigan Legislature has two full-time lobbyists, the City of Detroit one, Wayne County a part-timer and the state public service commission a part-timer.

New York state has a big group -- the city alone is beefing up its Washington lobby staff to six or seven -- they're virtually pikers compared to California.

Josiah Beeman, a shrewd Washington operative who gets $40,800 as the head of Gov. Edmund G. (Jerry) Brown Jr's lobbying office here (his official title is chief deputy director of finance), has four lobbyists plus support staff in his handsome set of offices at 600 Pennsylvania Ave. SE, just below the Capitol.

But that's barely a start, Beeman said he estimated that several dozen different jurisdictions in California have their own lobbyists. "If you got everyone who has anything to do with the state and its political subdivisions there are probably 30 to 35 plus support staff," he said.

He reeled off this list for starters: His own operation the governor's): the University of California system, which has its own full-time lobbyist, Peter Goldschmidt: the state college system; the state department of education; the City of Los Angeles: Alameda, Los Angeles, San Diego and Santa Clara Counties: a group of cities in Orange County: the Sacramento Utility District and the Westlands Water District; the state department of transportation; the state utilities commission; the state power commission, and the Metropolitan Water District of Southern California (one of the world's largest wholesalers of water).

Like Horn, Beeman has his tales of victory and achievement. Traer Sunley, his aide for health and welfare, was notified by the state welfare department that the federal aid to Indochina refugees was inadequate since the state of California has a big refugee population.

She helped serve as the liaison between state officials and Sen. Alan Cranston (D-Calif.), who eventually offered an amendment successfully boosting California's share from about $45 million (the Carter administration proposal) to $82 million over three years. Gov. Brown made some phone calls to Washington to help speed the bill through.

The amounts of money you deal with as a lobbyist for smaller and medium-sized cities are obviously far smaller than when you are lobbying for a giant state like California or New York, said Dick Cherry, director of the National Center for Municipal Development.

The national center is a nonprofit corporation established by the National League of Cities and U.S. Conference of Mayors, and its function, in effect, is to rent lobbyists to municipalities and give them backup facilities.

The national center has 16 lobbyists, and they represent 46 different cities --several having three to five cities to take care of. Cherry, 49, a former political science professor at Baylor, member of the Texas Legislature and one-time aide to Sen. Ralph Yarborough (D-Tex.), is the lobbyist for New Orleans. Others at the national center handle Anchorage, Phoenix, Toledo, Boston, Memphis, Bayamon (P.R.) and the like.

Cherry and researchers who help him seen the Congressional Record, the Commerce Business Daily, the Federal Register and similar publications each day to search for legislation, administrative rulemaking proposals, opportunities for grants and research contracts that affect New Orleans. "You have to know your local situation so well you will know how anything affects it."

He gave this example: when general revenue sharing was reenacted in 1976, Sen. Russell B. Long (D-La.) inserted a provision earmarking for the local sheriffs 7.5 percent of each parish's (county) revenue-sharing booty, to be matched by an equal amount from the state share. But since New Orleans sheriffs have little function (local city police handle law enforcement). Long exempted the city from the earmarking.

Cherry, looking at the bill, felt the city would be inadvertently shortchanged. It would lose the state matching portion. Cherry went to committee staff in the House and persuaded them to write a provision which, in effect, saved the state matching portion for New Orleans, giving the city $5.3 million more over three years than it would otherwise have received.

In a similar maneuver involving extension of the public works jobs bill, Cherry was instrumental in getting adoption of a provision allowing cities to obtain funding for new projects, not previously submitted, instead of only for those submitted the previous year.

He worked with Sen. J. Bennett Johnston Jr. (D-La.). Mayor Moon Landrieu, discovered New York had the same problem, and when Johnston propounded the new-project provision on the floor, the bill's floor manager. Moynihan, accepted it. New Orleans ended up with $11 million in projects instead of $4.4 million.

Of course, not everything is a win. Every time the Sun Belt and the Frost Belt knock heads over a distribution formula, someone wins and someone loses.

California's Beeman is pushing the idea of an irrigation canal from the Sacramento River to the Central Valley project that will cost the state and the United States each $3.5 billion, and "we're getting nowhere so far."

But it's a pretty good bet that those states and cities which are shelling out money for good lobbying representation in Washington are doing better in grabbing the federal buck than those who aren't.