Few, if any, of the many papers on turbulence spreading address the key question of how turbulence spreading actually affects the profile structure. Here, we are using a reduced model to answer that question. Turbulence spreading is most relevant near regions where the profiles support a strong intensity gradient ∇I. One such case is at the edge of an L mode discharge, near a source of turbulence [i.e., either a localized source of edge turbulence or an influx of turbulence from the scrape-off layer (SOL)]. Another is in “No Man's Land” (NML), which connects the pedestal to the stiff core in H mode. In the case of L mode, without an edge intensity source, the turbulence intensity profile is nearly flat and spreading has a weak effect. An edge localized source increases the edge ∇I, which then drives inward spreading. Invasion of turbulence from the SOL to the edge softens the edge pressure gradient. In H mode, the strong shear suppression of pedestal turbulence necessarily forces a sharp ∇I in NML. This sharp ∇I drives a significant flux of turbulence from the core to the pedestal, where it is ultimately dissipated by shearing. Counter-intuitively, the results indicate that spreading actually increases the pedestal height and width and hence the energy content in H mode. This suggests that models of the pedestal structure should include NML turbulence spreading effects. The relation of avalanches to spreading is studied. Spreading weakly affects the avalanche distribution, but the spatiotemporal correlation of intensity increases with spreading.