I think the organisation that ensures cooperation would also determine who runs the operational signalling at junctions and jointly used lines. The 'pre-grouping' vertical organisations and PTEs would do their own logistics and apply for slots with that organisation. The latter would not only regulate who provides and maintains jointly-used infrastructure but also what charges are made for doing so. One could call this organisation the 'Railway Clearing House'. As example, I think a future LNWR would include what is at present Virgin Trains and LNR and the NR organisations on those routes, and there would not be 'open access'*. However, the new LNWR would compete with HS2 and Chiltern. All three would be vertical organisations running track and trains along the lines I think were suggested by HH in his post. They would run their own train control and signalling except at junctions and joint lines, where the arrangements I suggest above would apply. *The new Railways Act would specify where low-cost inter-city services would be provided along the lines of Ouigo. They could be called 'Parliamentary trains' here.