  It is well known that a ramified holomorphic covering of a closed unitary
disc by another such a disc is given by a finite Blaschke product. The inverse
is also true. In this note we give an explicit description of holomorphic
ramified coverings of a disc by other bordered Riemann surfaces. The problem of
covering a disc by an annulus arises e.g. in multidimensional complex analysis;
we show that it may be effectively solved in terms of elliptic theta functions.
The covering of a disc by a flat domain is discussed in a monograph by Goluzin.
The machinery used here strongly resembles the description of magnetic
configurations in submicron planar magnets.
