I've always felt the propagation of the collapse was fairly obvious if you watched the copious number of videos.
After initiation the downward movement of the upper mass fell upon intact floors below and caused structural disintegration of these floors into the three basic component systems of the tower. Each of these three component systems behaved differently, and both video and the spread of debris after collapse confirms what happened:
EXTERIOR COLUMNS
The exterior columns were constructed in segments consisting of three columns, three stories high, connected by two spandrel plates. As such the exterior is best thought of not as a series of columns, but as a brickwork pattern of panels. Upon collapse initiation the collapse forces caused failure of the connections to the floor trusses, and these panels were forced outwards in chunks that broke away from the buildings. The size of these chunks varied - while single panels broke away there were also massive sections dozens of floors high and many panels wide that fell away intact and only then began to break up.
We can confirm this from videos, and also from the debris pattern. Most of the exterior panels were located in a fan pattern away from the building, with the upper most ones furthest away. It was almost exclusively the exterior panels which caused the severe damage to surrounding buildings.
FLOOR TRUSSES
With the exterior columns peeling away from the structure in great chunks, this left the light weight floor trusses very vulnerable and trying to absorb virtually the entire gravity load of the upper collapsing structure. These floor trusses were now only held up by their connections to the core of the structure, and under the loads they faced, these connections easily failed. This left the floor trusses to fall downwards onto lower trusses, causing a pancake type phenomenon as they crashed down on each other. If you think of them like square donuts stacked up on a central spike (the core) it gives you an idea of the mechanics of their failure.
There is some evidence that the floor truss collapse, requiring little force (only core connections needed to be broken) and being self-propagating (each failed truss would immediately join the mass falling on the truss below it) accelerated ahead of the visible collapse front, which would have further exacerbated the exterior column "peel away".
The fate of the floor trusses can be confirmed by eye witness testimony, and from the debris fields - most of the denser floor contents and truss material was located in close proximity to the building footprints, and the trusses themselves were found (according to NIST) stacked on top of each other in a heap at the base of each tower.
That leaves only our third component system:
BUILDING CORE
With the floor trusses and exterior columns breaking away that left only the core columns - the strongest part of the structure and also the component absorbing the least of the impact force (the strength of the core columns would have likely resulted in collapse material initially breaking either side of the core columns, much like a rock in a stream, thus protecting the core from much of the collapse force). And indeed, the core columns did in fact remain standing - for a time.
Of course simple physics will tell you that the cores alone - especially after the battering of the collapse - simply could not remain standing for any length of time. Tall thin structures are far too unsteady - which is why radio towers are stabilised with cables.
And so, the core structure failed at its weakest points which were the bolts and welds holding each three-storey section together.
The fate of the core columns is confirmed by video of the collapses which clearly shows the core of each tower still standing after the exterior columns and trusses had collapsed. It is further confirmed by the debris field - core columns were located in a scatter pattern around the building footprint, on the very top of the pile indicating they had fallen after everything else.
So there you have it. In simple terms, it went like this:
1. Collapse initiation
2. Exterior panels break away from truss assemblies
3. Truss assemblies break away from core structure
4. Core structure fails