  We present an Advanced Camera for Surveys/ Solar Blind Channel
far-ultraviolet (FUV) study of \h2 gas in 12 weak T Tauri stars in nearby
star-forming regions. The sample consists of sources which have no evidence of
inner disk dust. Our new FUV spectra show that in addition to the dust, the gas
is depleted from the inner disk. This sample is combined with a larger FUV
sample of accretors and non-accretors with ages between 1 and 100 Myr, showing
that as early as 1--3 Myr, systems both with and without gas are found.
Possible mechanisms for depleting gas quickly include viscous evolution, planet
formation and photoevaporation by stellar radiation fields. Since these
mechanisms alone cannot account for the lack of gas at 1--3 Myr, it is likely
that the initial conditions (e.g. initial disk mass or core angular momentum)
contribute to the variety of disks observed at any age. We estimate the angular
momentum of a cloud needed for most of the mass to fall very close to the
central object and compare this to models of the expected distribution of
angular momenta. Up to 20% of cloud cores have low enough angular momenta to
form disks with the mass close to the star, which would then accrete quickly;
this percentage is similar to the fraction of diskless stars in the youngest
star forming regions. With our sample, we characterize the chromospheric
contribution to the FUV luminosity and find that $L_{FUV}/L_{bol}$ saturates at
$\sim10^{-4.1}$.
