To alleviate the vast numbers of young adults between the ages of 19 and 29 with no health insurance, New York Gov. David A. Paterson is preparing a plan that will allow many more young adults to be claimed as dependents on their parents' health insurance plans. The plan was praised by some healthcare experts as a major step forward, but early evidence from the roughly two dozen other states that have adopted similar programs suggests that their effectiveness in shrinking the ranks of the uninsured has been modest at best.