Can parental rights over an adult be legally terminated? Can someone over 18 petition the court to terminate his/her parents’ parental rights? So that they’d no longer be legal next-of-kin, have intestate inheiritance rights (or ablity to contest a will), or be listed on a birth certificate?
Those are not parental rights, strictly, but merely next-of-kin rights.
IANAL-form Information regarding probable solutions: Will, durable power of attorney, and living will, specifying what you wish and who your attorney-in-fact empowered to act as next-of-kin is.
Consult a lawyer familiar with estate and familial law licensed in your jurisdiction.
In some places it is possible to formally declare a legal next-of-kin not the default one prescribed by law; in others, it is not.
Don’t worry about the birth certificate – other than its use as proof of your own birth, it has no legal bearing – i.e., who’s listed as father and mother on it is no longer of significance when one reaches one’s majority (except of course as proof of their next-of-kin status).
Important disclaimer: I am not a lawyer. Laws on this particular category of questions tend to vary even more than the typical variance in statutes from jurisdiction to jurisdiction. You need to consult with a local lawyer to do this stuff legally and ensure that what you create is binding.