What paperwork do we need signed by our partner that is leaving the company, and giving up his equity and rights to all projects he worked on?

On paper you have the advantage but after several startups control resides in he who knows how to execute the vision of the company.

This sounds as a deja vu to me. I have been in a similar situation back in 2000, we could only solve the issue thanks to a good mediator. However every situation is different and hence your route to a solution might be different. It also depends where you are in the world that defines how an email and/or verbal agreement might be a sufficient ground for legal actions. I am not a lawyer and can not judge that.

You should retain a lawyer, or another qualified individual, to act as the third party designee for the corporation (if you do not have a partner or co-owner who is a US citizen). The designee should prepare Form SS-4 (Application for Employer Identification Number) and Form 8821 (Tax Information Authorization) for the corporation’s president to sign and return.

I've discussed ideas with hundreds of startups, I've been involved in about a dozen startups, my business is at $1M+ revenue. The bad news is, there is no good way to protect ideas. The good news is, in the vast majority of cases you don't really need to. If you're talking to people about your idea, you could ask them to sign an NDA ("Non Disclosure Agreement"), but NDAs are notoriously hard to enforce, and a lot of experienced startup people wouldn't sign them. For example, if you asked me to sign an NDA before we discussed your Idea, I'd tell you "thanks, but no thanks". This is probably the right place though to give the FriendDA an honorable mention: http://friendda.org/. Generally, I'd like to encourage you to share your Ideas freely. Even though telling people an idea is not completely without risk, generally the rewards from open discussions greatly outweigh the risks. Most startups fail because they build something nobody wants. Talking to people early, especially people who are the intended users/customers for your idea can be a great way to protect yourself from that risk, which is considerably higher than the risk of someone taking off with your idea. Another general note, is that while ideas matter, I would generally advise you to get into startup for which you can generate a lot of value beyond the idea. One indicator for a good match between a founder and a startup is the answer to the question: "why is that founder uniquely positioned to execute the idea well". The best way to protect yourself from competition is to build a product that other people would have a hard time building, even if they had 'the idea'. These are usually startups which contain lots of hard challenges on the way from the idea to the business, and if you can convincingly explain why you can probably solve those challenges while others would have a hard time, you're on the right path. If you have any further questions, I'd be happy to set up a call. Good luck.

I'll keep try to keep this answer brief, but there are several factors and nuances that can be discussed in more depth. Where you decide to incorporate partly depends on what your future goals are with your company. Companies that plan to seek venture capital or go public typically choose Delaware as the state of incorporation, and usually choose a C-Corp. Delaware has a very well developed body of law surrounding corporate governance and that provides comfort and more certainty to future VC investors. If you're not planning to seek VC money any time soon, an LLC is a smart decision because of the tax benefits it can provide to you as the owner. It sounds like you want to grow your company on your own without outside financing. If that's the case, I would recommend forming your LLC in California. Regarding California vs. Delaware, one benefit to forming your LLC in California is that you can avoid paying a registered agent fee which can cost anywhere from $100-200 a year. If you plan to seek venture capital down the road, you can reincorporate in Delaware.