alt Hacker NewsIt is a gray area. What if you took Qt, removed macros, replaced anchoring with css for alignment, took all widget properties out into an entity component system and called it ET, could Trolltech complain? It is an entirely new design and nothing like they built. A ship of Theseus if you will.
The Ship of Theseus has nothing to do with the identity of the parts. That is not in question at all; they are explicitly different parts. The thought experiment is the question of the identity of the whole.
Qt in your example is a part. You're application is the whole. If you replaced Qt with WxWidgets, is your application still the same application?
But to answer your question, to replace Qt with you're own piecemeal code doesn't do anything more to Qt than replacing it with WxWidgets would: nothing. The Qt code is gone. The only way it would ship-of-theseus itself into "still being Qt, despite not being the original Qt" would be if Qt required all modifications to be copyright-assigned and upstreamed. That is absurd. I don't think I've ever seen a license that did anything like that.
Even though licenses like the GPL require reciprocal FOSS release in-kind, you still retain the rights to your code. If you were ever to remove the GPL'd library dependency, then you would no longer be required to reciprocate. Of course, that would be a new version of your software and the previous versions would still be available and still be FOSS. But neither are you required to continue to offer the original version to anyone new. You are only required to provide the source to people who have received your software. And technically, you only have to do it when they ask, but that's a different story.