are there any modern operating systems out there with no relation to UNIX

"Linux" is the kernel that launches the GNU userland, which is designed to be just like UNIX (but with freedums)
windows/DOS/whatever was based on some OS a hobbyist made, which was based on some obscure OS used in a university research lab, which was based on UNIX system III
OS X meets the single UNIX specification - Mac OS X is UNIX (more specifically, OS X is essentially a frontend to darwin, which is a mish-mash between UNIX, BSD and NeXTSTEP code, and Darwin is SUS compliant)

the only one i can think of is haiku, which is derived from beos, which was made to be POSIX compliant but not unix-derived, but haiku sucks and is going nowhere fast

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