One of the central goals of the Spitzer Legacy Project ``From Molecular Cores to Planet-forming Disks (c2d) is to determine the frequency of remnant circumstellar disks around weak-line T Tauri stars (wTTs) and to study the properties and evolutionary status of these disks. Here we present a census of disks for a sample of over 230 spectroscopically identified wTTs located in the c2d IRAC (3.6, 4.5, 4.8, and 8.0 um) and MIPS (24 um) maps of the Ophiuchus, Lupus, and Perseus Molecular Clouds. We find that ~20% of the wTTs in a magnitude limited subsample have noticeable IR-excesses at IRAC wavelengths indicating the presence of a circumstellar disk. The disk frequencies we find in these 3 regions are ~3-6 times larger than that recently found for a sample of 83 relatively isolated wTTs located, for the most part, outside the highest extinction regions covered by the c2d IRAC and MIPS maps. The disk fractions we find are more consistent with those obtained in recent Spitzer studies of wTTs in young clusters such as IC 348 and Tr 37. From their location in the H-R diagram, we find that, in our sample, the wTTs with excesses are among the younger part of the age distribution. Still, up to ~50% of the apparently youngest stars in the sample show no evidence of IR excess, suggesting that the circumstellar disks of a sizable fraction of pre-main-sequence stars dissipate in a timescale of ~1 Myr. We also find that none of the stars in our sample apparently older than ~10 Myrs have detectable circumstellar disks at wavelengths < 24 um. Also, we find that the wTTs disks in our sample exhibit a wide range of properties (SED morphology, inner radius, L_DISK/L*, etc) which bridge the gaps observed between the cTTs and the debris disk regimes.
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