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We consider a two-dimensional Ginzburg-Landau problem on an arbitrary domainwith a finite number of vanishingly small circular holes. A special choice ofscaling relation between the material and geometric parameters (Ginzburg-Landauparameter vs hole radius) is motivated by a recently dsicovered phenomenon ofvortex phase separation in superconducting composites. We show that, for eachhole, the degrees of minimizers of the Ginzburg-Landau problems in the classesof $\mathbb S^1$-valued and $\mathbb C$-valued maps, respectively, are thesame. The presence of two parameters that are widely separated on a logarithmicscale constitutes the principal difficulty of the analysis that is based onenergy decomposition techniques.

On approximation of Ginzburg-Landau minimizers by $\mathbb S^1$-valued maps in domains with vanishingly small holes