The wtc main support was provided by the central shaft, which in essence was a giant sized pillar (Like a tree trunk, but a little more complicated than that). Each slab also had "walls" which ran all the way to the exterior (in a cross shape from the center like you say. The pillars gave support and stability in between those for the floor above.
I think we are on the same page essentually. There is a blueprint around somewhere which shows how the towers were built.
Most of the weight of the floors was supported by the walls. The floor trusses themselves had essentially zero cantilever strength (meaning that if one end was unsupported, it would fall even if the other end was supported), and also meaning that unless the trusses were loaded non-uniformly (and I see no reason to believe that they were especially so) the ends of each truss would bear equal load. There were IIRC three "kinds" of truss. There were trusses that went from the central core to the exterior walls and supported only the weight of the floor in the immediate vicinity. Those trusses would put half their weight on the core and half on the exterior walls. There were trusses that went from the core to the wall and supported other trusses (basically four of these per floor). These would again put half their load on the core and half on the walls. Finally, there were trusses that went from the second group of trusses to the walls. These would put half their load on the wall, and half on the transfer trusses which in turn put half the load on the wall and half on the core. While the core did support a very large portion of the weight (including itself) the exterior walls bore more than half of the floor weight.