Kansas City, Mo. ? Lucia Harding learned years ago what to do when her W-2 arrived. Give it to her parents.

“It’s easier,” said the case manager for Big Brothers Big Sisters here. “I’m not math smart.”

With millions of similarly nonchalant teens and twentysomethings across the country, accountants and professional tax preparers may find themselves wide-eyed thinking about a prime demographic for industry growth. They’re offering free and cheap services, enticing them with specially designed Web sites, even offering discounts on vacations and electronics.

“The tax industry is not growing that fast,” said Tom Linafelt, a spokesman for Kansas City-based H&R Block, which is providing free online federal tax preparation for those 18 and under earning less than $10,000. “Hopefully we’ll be able to retain these clients for all their lives.”

Of about 126.8 million returns filed for the 2002 tax year, about 33.9 million — 27 percent — were from taxpayers under 30, according to the Internal Revenue Service.

IRS data shows about 91 percent of the roughly 18.4 million tax filers aged 18 to 24 earned an average refund of $939, though younger Americans are believed to be far more prone to miss out on the check by not filing.

Executives at TurboTax software maker Intuit recognized the trend and tried to determine the best way to address the demographic through research, focus groups and surveys.

They have launched a special site, RockYourRefund.com, complete with images of fun-loving, shirtless beachgoers and a grinning snowboarder, that offers what’s marketed as a fast, simple return for $5.95, “Because you’ve got better things to do.”

Users also can get discounts on travel and electronics purchases.

“They’re already online. They’re doing their shopping, online chatting,” said Colleen Ferrin, a San Diego-based spokeswoman for Intuit. “The next natural transition is to be doing things for their financial situation.”

High school senior Robin Lindquist navigates an H&R Block Web site offering free online tax preparation for young adults at her parent's home in Prairie Village. The program, offering free online services to workers 18 and under who earn less than 0,000, is part of a growing trend among tax preparers catering to young people.

H&R Block targeted the country’s youngest filers through its Web site, online banner ads and e-mails. Linafelt said the company was trying to lure teens whose parents manage their taxes and those who don’t bother filing taxes at all.

It’s not only the country’s biggest tax companies that are trying to lure in youthful customers.

Howell Financial Services, a two-person firm in Rockford, Ill., has placed ads in high school newspapers, offering free tax preparation for students. Hundreds of teens responded and many end up bringing their parents, too.

Eva Rosenberg, a Northridge, Calif., accountant, found similar success. She said young customers typically have simple returns for which she doesn’t charge much to prepare, though they often bring in more business.

“The kids turn out to have parents who are millionaires,” said Rosenberg, who runs a Web site, TaxMama.com. “Their parents start wondering why their kids are getting such better advice than they are.”

Rosenberg said she tries to explain the basics of taxes to her young clients, something the major firms are doing as well through their specially designed sites.

H&R Block and TurboTax both educate young filers with educational sections that explain, among other things, what W-2s and 1099s are, where taxes go, and how to take advantage of credits.

Steve Rochford, a former high school business teacher who taught teens about taxes, said these are questions many students can’t answer.

“I had kids coming up to me saying, “I got this in the mail,” and it would be a W-2,” he said. “They asked, ‘What do I do with it?”‘

Rochford now is an attorney with a tax law degree who authored a book called “Tax for Teens.” He said tax preparers’ outreach to young people is ingenious because their new clients will become accustomed to the convenience of having their taxes done.

“They become dependent on them and they have a lifetime client,” he said. “That’s smart.”