I can tell you what the role is not: the foolish source of money.
As defined, the corporate sets the strategic framework for the venture itself. It is therefore somehow connected to its core markets or strategic interests.
In my little world, the thought that corporate assets can magically be leveraged on a Company Building venture is only true in the mindset of the corporate itself, not in reality. At least not in the beginning.
During ideation the corporate sets the boundaries of the strategic scope of the venture. Even if everyone always states we're so out of the box and we're not limited to anything at all and be creative and do something completely different it is still at least implicitly the corporate that narrows it down. Why? Because you need to convince the corporate to fund the whole thing! Why should a professional business organization fund something that has exactly no strategic value now or in the future? If you cannot answer the "right to play" question, you won't get funding. So the corporate plays a very important role from the beginning: setting the direction!
As soon as an idea is born and becomes the core product of the venture the work mode changes. Now the Company Builder and its infrastructure, processes and resources take the lead and the corporate gives away the driver seat. Both parties will want to stick together closely anyway as you don't want to lose the connection here. Again: why should a corporate continue funding if there's no connection? So the corporate can play a strong role as door opener and as a source of reality check for the learnings in that phase. Everyone should be trying to prevent a limiting role of the corporate here as we're learning so much of the market during validation. A smart corporate will take the role of an aiding observer, learning and helping as much as possible, but from a backseat position.
Still the corporate doesn't take the lead, but investment sums get higher so there's more attention. In this phase, first business KPIs are developed and the corporate grows into the role of a shareholder. We tend to set up real shareholder meetings and reportings during that phase as the idea and business models turn more and more into a real venture. Also the investment managers on the corporate side will start to have closer looks at the venture now. So with incubation, the corporate takes over the advisory board seat and becomes an investor.
We have found a business model and rolled-out a first version. We have the first customers and know what we have to do. Let's start to build an organization. In this phase, staff ramp-up and process establishment takes place. It's very very hard for a corporate to not take the lead here as it sounds like the perfect playground - who knows how to build large organizational units better than a corporate? But hey, bad idea! We're still looking at a business model that is most likely completely different to everything within the existing organization. As a (majority) shareholder you will start to monitor the thing more and more. This phase is the critical one: if we get through without any damage we're ready to scale...
Now it's time to make a decision: is the business model to be owned completely by the corporate in the future or will we open up for more shareholders and investors to scale the company? The role of the corporate depends largely on that decision. If you want to own it, start to govern it! Make sure to give it as much power as possible to grow and decide what can be done to integrate the company. If you open up, be a shareholder with the interest of success but don't do anything to connect it to your strategy or your organization.