The battle is on to see if there will ever be a tobacco road in cyberspace.

As the White House leads a campaign to lower underage smoking rates by placing sweeping restrictions on cigarette advertising, giddy anti-smoking activists hope to stub out the tobacco industry’s on-line efforts before they can take root. But tobacco companies have started to claim their little acre of the Internet.

Nearly 37 percent of on-line Americans are under the age of 18, according to a study commissioned by HotWired, the on-line version of Wired magazine. That’s the same age group that President Clinton said on Aug. 10 …