It is highly unusual for placentae to be taken home and eaten. We never offer that service, if you have been asked if you want your placenta, it is to look at it, not devour it.
If someone asks for their placenta to take home then that is fine, but they must sign a legal document which states that it is their responsibility and they must dispose of it in the correct manner. Many cultures choose to bury their placentae as a fertility offering. The legal document will specify where the placenta can be buried eg, away from waterways etc.
Placentae are very nutritious and there are some interesting recipes on the web. Pate is quite easy to make from placentae and probably tastes no different than any other meat pate.
Before the days of HIV and other blood borne viruses, placentae were always saved and sent to drug companies. We had a big freezer for them on the old delivery suite and they were collected regularly. Hormones would be extracted from them and used to make medicines some componenets were allegedly added to cosmetics. One of the old retired (now deceased) midwives once told me that the membranes from placentae were once used as temporary skin grafts during the war.
A placenta is a remarkable organ and well worth a look if you get chance to see them. Many midwives will offer you a look at your placenta at delivery, if you get the opportunity then take a look at it. It is no different from viewing a good piece of liver in a butcher's shop so there's no need to be queasy about it. It is a multi-functional organ which controlls the baby's respiration, nutrition, hormones, growth, protection from some infections and drugs. It is the only organ which can comfortably perform all of these functions and more. To the trained eye every placenta looks slightly different......

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