Project networks are characterized by power law degree distributions, a property that is known to promote spreading. In contrast, the longest path length of project networks scales algebraically with the network size, which improves the impact of random interventions. Using the duplication-split model of project networks, I provide convincing evidence that project networks are fractal networks. The average distance between nodes scales as $\langle d\rangle \sim N^β$ with $0<β<1$. The average number of nodes $\langle N\rangle_d$ within a distance $d$ scales as $\langle N\rangle_d\sim d^{D_f}$, with a fractal dimension $D_f=1/β>1$. Furthermore, I demonstrate that the duplication-split networks are fragile for duplication rates $q<q_c=1/2$: The size of the giant out-component decreases with increasing the network size for any site occupancy probability less than 1. In contrast, they exhibit a non trivial percolation threshold $0<p_c<1$ for $q>q_c$, in spite the mean out-degree diverges with increasing the network size. I conclude the project networks generated by the duplication-split model are manageable for $q<q_c$ and unmanageable otherwise.