Algebroid functions, Wirsing's theorem and their relations

In this paper, we first point out a relationship between the Second Main Th eorem for algebriod functions in Nevanlinna theory and Wirsing's theorem in Diophantine approximation. This motivates a unified proof for both theorem s. The second part of this paper deals with "moving targets" problem for ho lomorphic maps to Riemann surfaces. Its counterpart in Diophantine approxim ation follows from a recent work of Thomas J. Tucker. In this paper, we poi nt out Tucker's result in the special case of the approximation by rational points could be obtained by doing a "translation" and applying the corresp onding result with fixed target. However, we could not completely recover T ucker's result concerning the approximation by algebraic points. In the las t part of this paper, cases in higher dimensions are studied. Some partial results in higher dimensions are obtained and some conjectures are raised.