The dozen biggest banks in Virginia now hold three quarters of the Commonwealth's bank deposits, according to a University of Virginia study that predicts tougher competition - and slower growth - for Virginia banks.

Deposit growth of Virginia banks slowed last year, the study discloses, and banks in urban areas are no longer growing as fast as their rural competitors.

Competition among banks, and between banks and savings and loan associations and credit unions will produce new options for Virginians looking for some place to put their money, the study suggests.

The statistical analysis of bank deposit trends was compiled by Charlotte H. Scott, a staff member of the University of Virginia's Tayloe Murphy Institute, an off-shoot of the Colgate Darden Graduate School of Business Administration.

In addition to compiling information on the amount of money deposited in banks in every Virginia city and county, Scott also shows how the big bank holding companies have come to dominate the business.

Scott's study produced this list of the 12 biggest banking companies total deposits and share of $16.5 billion of bank deposits in Virginia:

1) United Virginia Bankshares, $2.2 billion, 13.3 percent; 2) Virginia National Bankshares, $1.87 billion, 11.3 percent; 3) First Merchants Corp., $1.48 billion, 9 percent; 4) Dominion Bankshares Corp., $1.44 billion, 8.7 percent; 5) Bank of Virginia Co., $1.36 billion, 8.2 percent; 6) First Virginia Bankshares Corp., $1.12 billion, 6.8 percent.

7) Fidelity American Bankshares, $829 million, 5 percent; 8) Financial General Bankshares, $803 million, 4.9 percent; 9) Central National Corp., $441 million, 2.7 percent; 10) NE Corp., $270 million, 1.6 percent; 11) Southern Bankshares Inc., $253 million, 1.5 percent; 12) Valley of Virginia Bankshares, $202 million, 1.2 percent.

The 12 biggest bank's combined share of the market shrank slightly last year, from 75.3 percent of deposits in 1976 to 74.2 percent, Scott's study shows, and the banking industry's share of the savings market is also getting smaller.

In 1970 banks in metropolitan areas claimed 61 percent of the savings market - defined as the total of private savings deposits in banks and savings and loan associations and share balances in credit unions. Now the banks get only 51 percent of the savings bussiness in metropolitan areas, where competition is stiffest.

In the smaller urban areas of the state, the banks' share of savings has fallen from 87 percent to 78 percent. Even in rural areas, where the small town bank is the only game in town, the share is down from 98 to 95 percent.

A key factor is the movement of money out of banks into other savings institutions is the interest rate differential, the study says. Savings and loans can pay one quarter of one percent more than banks on regular savings accounts, and that is enough to influence today's sophisticated savers.

The University of Virginia economist notes that the number of families with incomes of more than [WORD ILLEGIBLE] is a key factor in analyzing bank competition in a particular market. "Higher income families are expected to have more savings and be more sensitive to the yield spread on alternative savings instruments," Scott explains.

Competition, she contends is being increased by the concentration of big banks.

Although economists usually equate competition with a lot of little companies, each scrambling for a piece of the action, it doesn't seem to work that way with banks. Individual banks, isolated in their local communities, tend not to compete with anybody.

However, bank holding companies with banks or branches in most major communities, have to be willing to fight for funds. In Virginia, Scott suggests, that competition is taking the form of extended banking hours, additional branches, 24-hour automated teller machines, lower checking account charges and additional consumer services.

Virginia has long permitted extensive branch banking and formation of bank holding companies and liberalized its banking laws even further this summer. The key change allowed banks that are merged into holding companies to add branches, like any independent bank. Previously a bank absorbed by a holding company lost much of its branching authority.

As a result several of Virginia's multi-bank holding companies plan to reorganize into one-bank operation, using one name throughout the state. Not only does this produce operating efficiencies but also it also creates a unified identity for the bank, a major plus in advertising and marketing. Scott predicts that electronic banking and the spread of automated teller machines will increase competition further.

Her forecast for Virginia Banking: "The heightened competition for deposit funds will make effective marketing strategies critical . . . Fewer banking markets will be insulated from competition . . . The public will have greater choice among equally accesible facilities in services differing in number and quality, and possibly also in price."