We have mapped the 1. 1 mm HCN J = 3 --> 2 line with IRAM 30 m telescope at 12'' resolution and the 63 mum [O I] P-3(1) --> P-3(2) line with the Kuiper Airborne Observatory at 20' resolution within a projected distance of 2 pc of IRS 16/SgrA*. The HCN J = 3 --> 2 data, together with the previous HCN J = 1 --> 0 data of Gusten et al., indicate that the circumnuclear molecular material is arranged in several kinematically distinct streamers. We find some evidence for a nearly complete ring of clouds, including the so far missing eastern continuation of the ''western arc,'' with an inclination of 70-degrees, a radius of 1.5 pc, and a rotational velocity of 110 km s-1. We infer a limit of about 19 km s-1 to any overall radial motion and systemic LSR velocity. A second feature with LSR velocities between +30 and +75 km s-1 lies northeast, east, and southeast of SgrA* and may represent material being fed from the massive +20/+50 km s-1 molecular clouds into the circumnuclear environment. West of SgrA* is a third feature with a radial velocity of about 70 km s-1, approximately constant with position. It is probably unrelated to the ring, but instead a separate cloud with a large radial velocity. The [O I] data reveal the presence of a large amount of neutral atomic gas inside the central ''ionized cavity,'' and associated with the '' northern '' and '' eastern '' arms of ionized gas. We estimate about 300 M. of dense neutral hydrogen gas within the 1.5 pc radius of the circumnuclear ring, about a factor of 10 more than the amount of ionized gas. The northern arm appears to be a bright, ionized rim at the surface of this neutral gas steamer, which is probably in the plane of the circumnuclear disk and falling from a gap in the 1.5 pc ring into the central 0.5 pc. We infer a mass inflow rate into the central parsec of 3 x 10(-2) M. yr-1. Almost all observed features of the spatial distribution of ionized, neutral atomic, and molecular gas in the central 2 pc of the Galaxy can be attributed to gas streamers rotating around or falling toward the Galactic center, and their illumination by several 10(6) L. of ultraviolet radiation produced within a few arcseconds of IRS 16/SgrA*.