  Motivated by recent experimental data on thin film superconductors and oxide
interfaces we propose a random-resistor network apt to describe the occurrence
of a metal-superconductor transition in a two-dimensional electron system with
disorder on the mesoscopic scale. We explore the interplay between the
statistical distribution of local critical temperatures and the occurrence of a
lower-dimensional (e.g., fractal-like) structure of a superconducting cluster
embedded in the two-dimensional network. The thermal evolution of the
resistivity is determined by an exact calculation and, for comparison, a
mean-field approach called effective medium theory (EMT). Our calculations
reveal the relevance of the distribution of critical temperatures for clusters
with low connectivity. In addition, we show that the presence of spatial
correlations requires a modification of standard EMT to give qualitative
agreement with the exact results.
