  We study the Ginzburg-Landau model of type-I superconductors in the regime of
small external magnetic fields. We show that, in an appropriate asymptotic
regime, flux patterns are described by a simplified branched transportation
functional. We derive the simplified functional from the full Ginzburg-Landau
model rigorously via $\Gamma$-convergence. The detailed analysis of the
limiting procedure and the study of the limiting functional lead to a precise
understanding of the multiple scales contained in the model.
