This thesis is based on three articles in the field of Several Complex Variables.The first article, which is joint work with M. El Kadiri, defines and studies the concept of maximality for plurifinely plurisubharmonic functions. Its main result is that a finite plurifinely plurisubharmonic function u on a plurifine domain U satises (dd^c u)^n = 0 if and only if u is plurifinely locally plurifinely maximal outside some pluripolar set.The second article is joint work with H. Peters, where we study sequences of holomorphic automorphisms of C^2 with a uniformly attracting fixed point. We find conditions under which the attracting basin of such a sequence is biholomorphic to C^2.In the third article, which is also joint work with H. Peters, we study Fatou components in attracting polynomial skew products. We identify a substantial class of such functions for which all Fatou components in the basin of the attracting fiber will eventually become periodic.