Results for d-2 percolation allow one to determine exactly the critical exponents for a polymer undergoing the special surface transition, while its bulk is at the THETA' point. Gamma-l = 8/7 and phi-s = 8/21 are the entropic and the crossover surface exponents, respectively. On the other hand, exact enumerations analysis leads to conjecture gamma-l = 4/7 at an ordinary THETA' point. This strongly supports universality of THETA and THETA' points. Similar exact results are obtained for a multicritical walk in the presence of correlated percolation vacancies.