A recent post discussed the general categories of rig types indigenous to Austronesia, and with further help from Wangka: Austronesian Canoe Origins, by Edwin Doran, Jr., we'll now see how the rig types and the hull types relate to one another. (All images here are from that source.)
The double spritsail, which some believe to have been the original Austronesian rig, was documented only in scattered locations in Indonesia (specifically, in Celebes and Sumatra), Sri Lanka, the Maldives, Madagascar, and on the Bab el Mandeb, the strait separating the Arabian Peninsula from Africa.
Doran neglects to identify the hull type associated with the double sprit rig, but he does so for the remainder of the rig types.
"I have come to believe that the presumed simplicity and primitiveness [of the double spritsail]are deceptive and that the sail represents an early but sophisticated attempt to devise a rig which will permit shunting. Without shifting the spars, the clew of the sail (after corner) becomes the tack (forward corner) on the other shunt, and a simple way of moving the center of effort of the sail has been developed. Micronesian crane sprit technique is more efficient once the sail is shifted, but requires a more cumbersome rig to achieve the same end."
The Oceanic sprit is associated with double canoes and tacking single outriggers, and appears in limited locations in Indonesia and the Philippines, and in New Zealand and parts of Polynesia, including Hawaii.
The crane sprit is used for most shunting single outriggers, mostly in Melanesia and Micronesia, but also in parts of Polynesia:
The boom-lug rig is used almost exclusively with double-outrigger canoes, whose domain is primarily Indonesia and Malaysia, with extensions into Melanesia and a couple of outliers in the Philippines and the Persian Gulf:
Doran uses these distribution maps to attempt to deduce the relative ages of the various rig types, their places of origin, and their role in the evolution of the other types -- i.e., which rig type and hull type came first, and how and where they evolved into the other types. I don't find his arguments strongly convincing, however, so I will refrain from describing them.