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We address the crystallization of monodisperse hard spheres in terms of the properties of finite-size crystalline clusters. By means of large scale event-driven molecular dynamics simulations, we study systems at different packing fractions phi ranging from weakly super-saturated state points to glassy ones, covering different nucleation regimes. We find that such regimes also result in different properties of the crystalline clusters: compact clusters are formed in the classical nucleation theory regime (phi <= 0.54), while a crossover to fractal, ramified clusters is encountered upon increasing packing fraction (phi >= 0.56), where nucleation is more spinodal-like. We draw an analogy between macroscopic crystallization of our clusters and percolation of attractive systems to provide ideas on how the packing fraction influences the final structure of the macroscopic crystals. In our previous work (Phys. Rev. Lett., 2011, 106, 215701), we have demonstrated how crystallization from a glass (at phi > 0.58) happens via a gradual (many-step) mechanism: in this paper we show how the mechanism of gradual growth seems to hold also in super-saturated systems just above freezing showing that static properties of clusters are not much affected by dynamics.