No! They leave the prostate just where it is.
Since it encircles the urethra it's in a very tricky place.
Removing it can easily cause incontinence.
That's why prostate cancer can be a very big deal, (besides killing you).
Don't worry, on female hormones the incidence of prostate cancer goes way down.
The prostate gland excretes a small amount of prostatic fluid, i.e. "pre-cum".