  In this paper we develop a blow up analysis for solutions of a planar
semilinear elliptic equation involving exponential nonlinearities. Such
solutions describe cosmic strings, and we show how their blow up behaviour is
characterised by new and surprising phenomena. For example in some cases, the
blow up profile of the solution is described in terms of a differential problem
that bares a geometrical meaning in the context of the uniformization of the
Riemann sphere with conical singularities.
