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Some scenarios for planetesimal formation go through a phase of collapse of gravitationally bound clouds of mm-cm-sized pebbles. Such clouds can form for example through the streaming instability in protoplanetary disks. We model the collapse process with a statistical model to obtain the internal structure of planetesimals with solid radii between 10 and 1,000 km. In the collapse, pebbles collide and, depending on relative speed, collisions have different outcomes. A mixture of particle sizes inside a planetesimal leads to better packing capabilities and higher densities. In this paper we apply results from new laboratory experiments of dust aggregate collisions (presented in a companion paper) to model collision outcomes. We find that the internal structure of a planetesimal is strongly dependent on both its mass and the applied fragmentation model. Low-mass planetesimals have no/few fragmenting pebble collisions in the collapse phase and end up as porous pebble-piles. The amount of fragmenting collisions increases with increasing cloud mass, resulting in wider particle size distributions and higher density. The collapse is nevertheless "cold" in the sense that collision speeds are damped by the high collision frequency. This ensures that a significant fraction of large pebbles survive the collapse in all but the most massive clouds. Our results are in broad agreement with the observed increase in density of Kuiper belt objects with increasing size as exemplified by the recent characterization of the highly porous comet 67P/Churyumov-Gerasimenko., Comment: in APJ 2016