After years, are transplanted organs replaced with some or all of your own tissue?

No: Transplanted organs remain what they are. That's why patients will require lifelong anti-rejection drugs.

Yes they are!: This phenomenon is seen in many long-term successful transplant recipients. It was hoped that accelerating the development of this "chimerism" would help patients by lowering the risk of rejection and possibly allowing patients to decrease or eliminate their anti-rejection medicines. Unfortunately, this strategy has not been very successful and nearly all patients must take their meds for life.

Interesting question: Very interesting question. This is called chimerism in medical terminology ( two tissues from different sources) living together. In reality some host cells may interlace with the donor tissue, i.e. White blood cells, small blood vessel cells, etc. But the donor organ will not be "replaced" by the host tissues.