Beneath Yellowstone: Two large blobs of hot material from the mantle (in yellow) are melting rock closer to the surface (orange), creating pools of hot material (red and orange) that power hydrothermal systems and previous eruptions, and may be the sites of future activity.
Credit: Bennington, et al.
Although together they contain a lot of molten basaltic material (between 4,000 and 6,500 cubic kilometers), it is not very concentrated. Instead, these are usually relatively small amounts of molten material traveling through cracks and fractures in solid rock. This keeps the concentration of molten material below the limit necessary to enable eruptions.
After the two streams of basaltic material merge, they form a reservoir containing a significant amount of molten crustal material, which means rhyolitic. The amount of rhyolitic material here is at most less than 500 cubic kilometers, so it could produce a large eruption, albeit a small one by historic Yellowstone standards. But again, the fraction of molten material in this volume of rock is relatively low and is not considered likely to lead to eruptions.
From there to the surface there are several distinguishing features. Relative to the hotspot, the North American plate above it is moving westward, which historically means the location of eruptions has moved from west to east across the continent. Accordingly, to the west of the bulk of the surface molten material there is a pool that no longer appears to be connected to the rest of the system. It is small, with only about 100 cubic kilometers of material, and too diffuse to support a large eruption.
Future risks?
There is a similar blob of molten material on the surface that may not currently be connected to the rest of the molten material south of it. It's even smaller, probably less than 50 cubic kilometers of material. But it's located just below a large blob of molten basalt, so it's likely to receive a fair amount of heat input. This site also appears to have fueled the most recent major eruption in the caldera. So while it may not cause a major eruption today, it is not possible to rule out the location for the future.
