Children who grow up in homes with severe problems such as poverty, parents with little formal education, marital discord, divorce, alcoholism or mental illness face an uphill struggle to become healthy, well-adjusted adults. To find out why some of these children do grow up to become competent, caring adults, Emmy E. Werner, a nationally recognized professor of human development at UC Davis, has been tracking the lives of 505 men and women since they were born in Kauai, Hawaii, in 1955. In her latest book, written with Ruth Smith -- "Overcoming the Odds" (Cornell University Press, 1992) -- Werner states that one of the most important factors in helping vulnerable children overcome various and chronic disadvantages is supportive relationships. The presence of at least one competent person who accepted the child unconditionally and was available as a source of reassurance and comfort during stressful times can make a critical difference. As young adults, many of the high-risk individuals in the study turned their fortunes around through community colleges, the armed forces or involvement in a church or religious community. Werner suggests their experiences provide lessons for intervention programs.