Transitional disks are protoplanetary disks around young stars, with inner holes or gaps which are surrounded by optically thick outer, and often inner, disks. Here we present observations of 62 new transitional disks in the Orion A star-forming region. These were identified using the \textit{Spitzer Space Telescope}'s Infrared Spectrograph and followed up with determinations of stellar and accretion parameters using the Infrared Telescope Facility's SpeX. We combine these new observations with our previous results on transitional disks in Taurus, Chamaeleon I, Ophiuchus and Perseus, and with archival X-ray observations. This produces a sample of 105 transitional disks of "cluster" age 3 Myr or less, by far the largest hitherto assembled. We use this sample to search for trends between the radial structure in the disks and many other system properties, in order to place constraints on the possible origins of transitional disks. We see a clear progression of host star accretion rate and the different disk morphologies. We confirm that transitional disks with complete central clearings have median accretion rates an order of magnitude smaller than radially continuous disks of the same population. Pre-transitional disks --- those objects with gaps that separate inner and outer disks --- have median accretion rates intermediate between the two. Our results from the search for statistically significant trends, especially related to $\dot{M}$, strongly support that in both cases the gaps are far more likely to be due to the gravitational influence of Jovian planets or brown dwarfs orbiting within the gaps, than to any of the photoevaporative, turbulent or grain-growth processes that can lead to disk dissipation. We also find that the fraction of Class II YSOs which are transitional disks is large, 0.1-0.2, especially in the youngest associations.
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