How is traffic allocated by the exchanges to different DSPs?

As I understand it, it is a common aspect of media buying that once you have a profitable campaign, you should scale to other traffic sources, including other DSPs. However, most of these DSPs connect to the same ad exchanges.

Do all the DSPs have access to all of the inventory of each exchange, and that traffic is split in real time by bids to the different DSPs or are placements or certain amounts of traffic allocated to specific DSPs such that you can scale the same campaign to another D ...