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We analyse a blow-up sequence of solutions for Liouville type equationsinvolving Dirac measures with "collapsing" poles. We consider the case whereblow-up occurs exactly at a point where the poles coalesce.  After proving that a "quantization" property still holds for the "blow-upmass", we obtain precise point-wise estimates when blow-up occurs with theleast blow-up mass.  Interestingly, such estimates express the exact analogue of those obtainedfor "bubble" solutions of "regular" Liouville equations, when the "collapsing"Dirac measures are neglected. Such information will be used to describe theasymptotic behaviour of minimizers of the Donaldson functional introduced byGoncalves and Uhlenbeck (2007), yielding to mean curvature 1-immersions ofsurfaces into hyperbolic 3-manifolds.

On the blow-up analysis at collapsing poles for solutions of singular Liouville type equations