No, parents are generally
not legally responsible for their adult children's tuition. Once a child reaches the legal age of adulthood (18 in most US states), they are considered financially independent. There's no legal obligation for parents to pay for their college or other post-secondary education.
While many parents *choose* to help their adult children with tuition, it's a matter of personal choice and financial capability, not a legal requirement. Any financial support provided is generally a gift, not a legally enforceable obligation.