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(Abridged) Dust particles evolve in size and lattice structure inprotoplanetary disks, due to coagulation, fragmentation and crystallization,and are radially and vertically mixed in disks. This paper aims at determiningthe mineralogical composition and size distribution of the dust grains in disksaround 58 T Tauri stars observed with Spitzer/IRS. We present a spectraldecomposition model that reproduces the IRS spectra over the full spectralrange. The model assumes two dust populations: a warm component responsible forthe 10\mu m emission arising from the disk inner regions and a colder componentresponsible for the 20-30\mu m emission, arising from more distant regions. Weshow evidence for a significant size distribution flattening compared to thetypical MRN distribution, providing an explanation for the usual boxy 10\mu mfeature profile generally observed. We reexamine the crystallinity paradox,observationally identified by Olofsson et al. (2009), and we find asimultaneous enrichment of the crystallinity in both the warm and cold regions,while grain sizes in both components are uncorrelated. Our modeling results donot show evidence for any correlations between the crystallinity and either thestar spectral type, or the X-ray luminosity (for a subset of the sample). Thesize distribution flattening may suggests that grain coagulation is a slightlymore effective process than fragmentation in disk atmospheres, and that thisimbalance may last over most of the T Tauri phase. This result may also pointtoward small grain depletion via strong stellar winds or radiation pressure inthe upper layers of disk. The non negligible cold crystallinity fractionssuggests efficient radial mixing processes in order to distribute crystallinegrains at large distances from the central object, along with possible nebularshocks in outer regions of disks that can thermally anneal amorphous grains.

C2D Spitzer-IRS spectra of disks around T Tauri stars V. Spectral decomposition