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We study the evolution of the ionization state of the IGM at the end of thereionization epoch using spectra of a sample of nineteen quasars at 5.74<z<6.42discovered in the SDSS. Three methods are used to trace IGM properties: (a) theevolution of the Gunn-Peterson optical depth in the Ly alpha,beta, and gamma;(b) the distribution of dark absorption gaps, and (c) the size of HII regionsaround quasars. We find that the evolution of the IGM accelerated at z>5.7: theoptical depth evolution changes from tau ~ (1+z)^{4.3} to (1+z)^{>11}, and theaverage length of dark gaps with tau>3.5 increases from <10 to >80 comovingMpc. The dispersion of IGM properties along different lines of sight alsoincreases rapidly, implying fluctuations by a factor of >4 in the UV backgroundat z>6, when the mean free path of UV photons is comparable to the correlationlength of galaxies. The mean length of dark gaps shows the most dramaticincrease at z~6, as well as the largest varianace. We suggest using dark gapstatistics as a powerful probe of the ionization state of the IGM at yet higherredshift. The sizes of HII regions around quasars decrease rapidly towardshigher redshift, suggesting that the neutral fraction of the IGM has increasedby a factor of >10 from z=5.7 to 6.4. The mass-averaged neutral fraction is1-4% at z~6.2 based on the GP optical depth and HII region sizes. Theobservations suggest that z~6 is the the end of the overlapping stage ofreionization, and are inconsistent with a neutral IGM at z~6, as indicated bythe finite length of dark absorption gaps.Comment: AJ, in press, 58 pages, 15 figures; revisions in section on quasar  HII region

Constraining the Evolution of the Ionizing Background and the Epoch of Reionization withz ~ 6 Quasars. II. A Sample of 19 Quasars