The investment banking firm of Salomon Brothers Inc. was easily the top manager of public securities offerings in 1984 for the second year in a row, more than doubling the underwriting totals of its closest competitor, according to IDD Information Services Inc. of New York.

Salomon led the investment banking underwriters by raising a total of $21.2 billion for its clients in 186 offerings.

Drexel Burnham Lambert Inc. finished second by raising $10.5 billion through 102 offerings, many of which were "junk bond" offerings of below-investment-grade securities.

First Boston Corp. finished third, raising about $10 billion in 129 offerings, followed by Merrill Lynch Capital Markets, which raised $8.6 billion in 125 offerings. Goldman, Sachs & Co. was next on the list, followed by Shearson Lehman/American Express, Morgan Stanley & Co., Kidder, Peabody & Co., Prudential Bache Securities and Paine Webber Mitchell Hutchins.

For the year, there were 1,410 debt and stock issues totaling $82.2 billion, down from 2,196 issues totaling $97.1 billion in 1983.

Last year was the second-busiest year overall for underwritings, although the market for stock offerings dropped off dramatically from the prior year.

The overall rankings include both debt and stock offerings. Morgan Stanley was the lead manager in bringing common stock issues to market, raising $1.2 billion as the lead manager of 17 offerings.

Morgan Stanley managed the three largest offering by foreign companies last year, including the initial public offering by British Telecommunications PLC.

Salomon's strength as the top lead manager was confirmed by its role as the chief investment banker underwriting mortgage-backed securities, a market that has grown dramatically in recent years.

Salomon managed more than $4 billion of mortgage-backed offerings.

Overall, in the debt markets, firms raised $62.25 billion in 718 offerings in 1984 versus $46.06 billion in 534 offerings in 1983.

Stock offerings fell dramatically from a record 1,418 offerings in 1983 that raised $36.65 billion to 556 offerings in 1984 that raised $8.92 billion.

Investment banking firms profit through underwritings by acting as wholesalers of securities, purchasing securities from corporations that wish to raise money in the public markets and reselling these securities to the public.

Typically, one or two firms serve as the lead manager of an offering and pool their risk by inviting other firms to participate in the underwriting.