OK, I was contracting in my previous life so I've seen these issues pop up many times before. Here's few words.
A) is illegal. You have no ownership of ANY code or IP that you work on at the company that employs you. That's what they're paying you for, after all.
B) is also illegal. Unless the company in question has open sourced their code and allows anyone to use it under some kind of a BSD-like license, you have absolutely no right to use that code or IP.
Not only are both of these cases illegal, they're also highly unethical. Also, if you're forming a company around someone else's IP, you're gonna crash and burn.
When I worked as a contractor, I would use my own libraries to save me some time but before I used them, I notified the management that I was using them and told them that I own the code and that I give them full right to use it without any licensing fees and I also told them I would use them on my other contracting jobs. They always accepted these stipulations an I've never had any problems. They loved the fact that I was not wasting my time and their money re-implementing the wheel and that I was solving their problems in record time. The key is to be open and put it all on the table before you start working.
Also, after I'd finish working on a project and if I was using my own computer, I'd wipe my computer clean of all of their code. I would do that on the last day of my job and I ALWAYS made sure that someone from the management was there to witness it. Sure, that might be going overboard but trust me... it's worth it. It shows them that you care about these sorts of things and it also makes sure that they won't have a strong case if they ever decide to sue you down the road because you end up inventing something amazing that's in their marketspace or you end up working for competition.