In two previous papers [Math. Z. 170, 195-216 (1980; Zbl 0411.30010) and Ann. Univ. Mariae Curie-Skłodowska, Sect. A 36/37 (1982-83), 33-43 (1983; Zbl 0572.30020)] we studied the class \(S_ 0\) of functions f analytic, univalent, and nonvanishing in the unit disk D, with \(f(0)=1\). Among other things we investigated coefficient problems and the qualitative properties of support points. Here we continue this work with several new results. First we make the observation that the asymptotic form of Littlewood's coefficient conjecture actually implies Littlewood's conjecture. Turning next to support points, we show that the arc \(\Gamma\) omitted by a support point of \(S_ 0\) is always asymptotic to a line at infinity. Essentially the same argument gives the corresponding result for the Montel class \(M_ r\) of functions f analytic and univalent in D with \(f(0)=0\) and \(f(r)=1\), where \(0