Traveling over the global computer web called the Internet, the Phoenix law firm's ad flew across continents and oceans. It reached as far as Germany, Australia, South Africa and Denmark to deliver a query: Do you want to get a green card for permanent residence in the United States? "THE TIME TO START IS NOW!!"

Responses came flooding in by electronic mail -- they numbered 35,000 within days. Some were polite requests for more information. But many were hate mail, sent by Internet users furious that the network's near-sacred restrictions on advertising were being trampled.

One angry soul made the point by sending 8 million characters of gibberish -- a "mail bomb" intended by its sheer size to gum up the computer used by the law firm, a husband-and-wife operation called Canter & Siegel.

How will ads fare on the information highway as it unfolds in the future? The Internet, moving text and occasionally sounds and images between computers at high speed, is the closest thing today to that highway. What happens there may shape any coming networks that connect to homes and offices. The Internet was established as a private channel for researchers and academics. Today, anyone with a properly outfitted computer and the subscription fees can get on, but sentiments against commercialism remain strong.

Law firm partner Laurence Canter dismisses the critics as "people who have had the computer networks as their private world for a long time." Resistance to ads is outmoded and will change, he predicted.

Most analysts agree that more ads are coming. Used by roughly 20 million people worldwide, many of them with higher-than-average education and income, the network is simply too tempting a place for advertisers to ignore. Moreover, as the network expands, it will need new sources of income.

Most companies will avoid the scattergun approach of Canter & Siegel, many analysts predict. "Mass advertising gets you hated," said Mark Gibbs, a consultant who advises on using the Internet. "It's only for the thick-skinned."

The network already designates electronic locations where ads, subtle or otherwise, are accepted. The common trait is that the consumer must reach out and collect the information, rather than have it arrive uninvited.

Companies can create public databases offering topical information, with ads for their products or services mixed in. Tourist information in an Internet database in Thailand, for instance, includes the names and telephone numbers of hotels.

Canter & Siegel's ad was aimed at the thousands of Internet bulletin boards, electronic meeting places where people "post" messages for anyone to see or read.

A few boards are formally designated as markets, generally for second-hand goods. But most exist for words -- fact and opinion on defined subjects as diverse as microbiology, Star Trek trivia and problems of programming in a particular computing language.

To Canter, the Internet bulletin boards were an ideal, low-cost and perfectly legitimate way to target people likely to be potential clients. Many Internet users are foreigners in need of immigration services, he said. And messages flow over the Internet almost for free.

"I can't think of any other way to reach that many people who have things in common without spending thousands of dollars," he said.

So the firm compiled a list of virtually all the bulletin boards in the world. It created special software that sent the ad to roughly 6,000 bulletin boards. Transmission took just an hour and a half last Monday night.

The ad informed people that the United States was about to conduct a lottery to issue 55,000 green cards. People responding to the offer of free information received a six-page description and an offer by the firm to handle the paperwork, said Canter.

But posting a message that is off a board's subject is a serious breach of network etiquette -- and advertisements are particularly unwelcome. The offense is sure to get the perpetrator and anyone viewed to have helped out "flamed," Internet argot for showered with angry messages.

Jeff Wheelhouse, system administrator of Internet Direct, a Phoenix company that Canter & Siegel paid for Internet access, said he arrived at work last Tuesday morning to find hundreds of messages taking his firm to task for allowing the ad to go out.

Other messages were flooding in to the law firm, so many, Wheelhouse said, that Internet Direct's computer crashed more than a dozen times. On the grounds that they had abused their privileges, Wheelhouse revoked Canter & Siegel's account. "They took 15 or 20 years of Internet tradition and said the hell with it," he said.

But mail kept arriving. Internet Direct stored almost 30,000 messages on magnetic discs, Wheelhouse said, leading Canter & Siegel to threaten the company with a lawsuit if the messages weren't turned over.

Out on the net, thousands of people were outraged, though here and there was grudging respect for what was seen as the firm's diabolical thoroughness.

"You, Laurence Canter, make me sick," wrote one user. "This idiot posted this to every news group," wrote another. "Please flame him by e-mail at will."

But others sent messages asking for more information about the service. Canter says that about three-quarters of the mail that arrived before the shut-off requested more information. The firm plans more Internet advertising. And other companies have been in touch, Canter said, to ask how they can do the same.