A structural model is developed for describing the solid-state transformation of a vertically oriented carbon multiwall nanotube (MWNT) forest to a horizontally oriented MWNT sheet or yarn. The key element of our model is a network of individual carbon nanotubes or small bundles interconnecting the array of main large-diameter MWNT bundles of the forest. The dry-draw self-assembly mechanism for MWNT sheet formation involves two principal processes that reconfigure the interconnection network: (1) unzipping by preferentially peeling off interconnections between the bundles in the forest and (2) self-strengthening of these interconnections by densification at the top and bottom of the forest during draw-induced reorientation of the bundles. It is shown that interconnection density is a key parameter that determines the ability of a MWNT forest to be dry-drawable into sheets and yarns. This model describes the principal mechanism of solid-state draw (confirmed by dynamic in situ scanning electron microscopy), the range of forest structural parameters that enable sheet draw, and observed dependencies of sheet properties on the parent MWNT forest structure.