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In this paper we consider a cooperative wireless network where each terminal communicates to a destination node with the aid of multiple relaying nodes. The focus is on cooperative transmission protocols that are based on the simultaneous transmission by a number of cooperating nodes. Outage performances are analyzed by assuming a distributed randomized orthogonal space-time coding scheme (DR-OSTC) to be employed by the relaying terminals during the transmission session. The DR-OSTC scheme requires that each cooperating node chooses randomly and independently to serve as one of the space-time virtual antennas. By avoiding any pre-defined terminal-to-codeword mapping, the random selection of the space-time codewords substantially reduces the needed control overhead with respect to other distributed space-time coding strategies simplifying the node coordination task. According to this scheme, in this paper it is tackled the problem of designing both the minimum number of cooperating nodes M and the spatial dimension L of the space-time code matrix so as to meet a specific outage probability requirement at the destination. Outage performances are also analyzed by developing simple but effective design rules tailored for two cooperative transmission protocols in realistic propagation environments.