PORTLAND, Ore. (AP) - More than a dozen adoptees hoping to track down their birth parents showed up at the Oregon Health Division today, the first day the state was able to begin processing their requests for birth certificates."I think everyone who has come in has been shaking this morning," said Phyllis Mason, who manned the desk at the agency's Vital Records Department. "A lot of emotions are involved in this."Kim Porter, 34, of Oregon was among those who appeared in person to turn in her application for a birth certificate. She was unfazed to discover it would take six to eight weeks to receive it as the agency processes the 2,334 applications it had received by 9 a.m. today in the order they were received."I've been waiting 34 years so I don't think another six weeks will make any difference," Porter said.Those whose applications are on the top of the stack could have their birth certificates by early next week, said Mel Kohn, deputy state epidemiologist. On Tuesday, U.S. Supreme Court Justice Sandra Day O'Connor rejected an emergency request to delay Oregon's 1998 adoption records law from going into effect. The law went into effect at 5:01 p.m. Tuesday, after the close of the business day, a deadline that had been set earlier by a lower court.The decision ended two years of court battles begun by six women who argued the new law violates the privacy of people like themselves who gave up their children for adoption and started new lives.Adoptees can find the application for their original birth certificates on the Internet. Birth mothers do have some say in the process. They can download from the Internet a "contact preference form" that would be sent to adoptees along with their birth certificates.The form gives birth mothers an opportunity to say they want to be contacted, prefer only to be contacted through an intermediary or do not wish to be contacted. If they choose the last option, they also must file a detailed family medical history.Thomas McDermott, a lawyer for the law's backers and the adoptive father of a 16-year-old boy, was jubilant Tuesday that his son and others would have the chance to learn about their pasts."What I've seen with my son is that he really yearns for a more complete picture of himself," he said. "It's a basic human right to know your heritage."Frank Hunsaker, attorney for the six anonymous birth mothers, was bitter about the removal of the last legal roadblock, saying his clients "are extremely disappointed and scared and even angry that their rights have been ignored."He said giving adult adoptees access to their original birth certificates violates an implied contract the birth mothers thought they had--that their identities would be protected and that they would never be contacted by the children they relinquished.In 1997, the U.S. Supreme Court refused to review a similar open adoption records law from Tennessee, although that law was passed by the Legislature, not by the voters.Tennessee and just three other states--Alaska, Delaware and Kansas--allow adult adoptees access to original birth certificates, which often have birth parents' names. A similar law in Alabama was just signed by the governor and will go into effect until Aug. 1.