Carbon nanosheets are a unique nanostructure that, at their thinnest configuration, approach a single freestanding graphene sheet. Temperature desorption spectroscopy (TDS) has shown that the hydrogen adsorption and incorporation during growth of the nanosheets by radio frequency plasma-enhanced chemical vapor deposition are significant. A numerical peak fitting to the desorption spectra (300-1273 K) via the Polanyi-Wigner equation showed that desorption followed a second order process, presumably by the Langmuir-Hinshelwood mechanism. Six peaks provide the best fit to the TDS spectra. Surface desorption activation energies were determined to be 0.59, 0.63, and 0.65 eV for the external graphite surface layers and 0.85, 1.15, and 1.73 eV for desorption and diffusion from the bulk. In contrast to TDS data from previously studied a-C:H films [Schenk et al. J. Appl. Phys. 77, 2462 (1995)], a greater amount of hydrogen bound as sp(2) hybridized carbon was observed. A previous x-ray diffraction study of these films has shown a significant graphitic character with a crystallite dimension of L(a)=10.7 nm. This result is consistent with experimental results by Raman spectroscopy that show as-grown carbon nanosheets to be crystalline as commercial graphite with a crystallite size of L(a)=11 nm. Following TDS, Raman data indicate that the average crystallite increased in size to L(a)=15 nm.