Does anyone know anything about donating one's dead body for medical research?

I am putting my affairs in order now, and I would like to do this. I am looking into it; it saves the cost of burial or cremation while promoting medical teaching and research.

Apparently some companies/brokers are more reliable than others. Anyone know anything about this?

Two factors I am concerned with: The reliability of picking up the body from the place of death (I've heard that sometimes they say, "Our morgue is full. You'll have to wait three months" or something like that). And how soon they would return the cremains to the relative or person designated to receive them. Some say about 5 weeks, some say 2-3 years.