On the possible rate of growth of polynomials orthogonal with a continuous positive weight

It is proved that there are continuous positive weights such that the orthogonal polynomials constructed with respect to them are not uniformly bounded at a given point, both for the circle and for a closed interval. Furthermore, in the case of the circle the orthogonal polynomials have logarithmic growth. Also determined is a minimal (in a certain sense) class of positive continuous functions in which there exists a weight function having the property indicated.