study of supersymmetric black-hole solutions, there are important questions that remain unanswered or whose answer is unclear. For instance, we know how to construct many supersymmetric black-hole-type solutions, but many of them are singular. Some of these become regular when string corrections are taken into account and for all the regular black hole solutions we seem to have a String Theory model that accounts for its entropy. How are the other singular solutions to be understood? How can it be that they are supersymmetric and yet there is no String Theory model for them? Or, if there is, why are they singular?

The main goal of this paper is to try to answer this question by giving a set of conditions that supersymmetric black-hole-type solutions must satisfy in order to be admissible in the context of $N=2,d=4$ supergravity coupled to vector supermultiplets. Admissible solutions will be regular and will describe one or several black holes in static equilibrium, even though the system may have a finite global angular momentum, as is for example the case in the solution constructed in Ref. [@Elvang:2005sa]. Furthermore, we expect only admissible solutions to have a miscroscopic String Theory model. We will argue that the 