Caponizing has not tradtionally been done with anesthesia. As far as I know there is nothing available to do it that way. The bird is simply splayed out in the right way, the proper tools are brought to bear and the surgery quickly done. It takes less than 30 seconds for a skilled practitioner. When it is done, the bird is released to go on its merry way.
Caponisers were once respected men and paid by the bird, making the rounds in a district as they plied their trade. A good one could make a tidy days wage in season. The practice is still very popular in France, Italy and Turkey.
The capon, a male 'sans testicles', is reared like any other meat bird - for that is what he is. He is held separate from the rest of the flock with is fellow capons and essentially mollycoddled. Think Kobe Beef and you get the idea.
The process is not solely intended to fatten the bird, although that is a side benefit. Rather, caponizing eliminates testosterone in the bird and thus fibroid tissue within the musculature never develops. This makes for a tender, soft and succelent flesh at the table.
There was once a subdermal, hormonal application that chemically rendered a cock a capon. Better living through chemistry, I suppose!
But food purity laws outlawed the practice several decades ago.
The capon is allowed to grow longer than other meat birds, as long as 8 months for the largest ones. In this time he will grow several pounds heavier than a normal cock, reaching 10-12 lbs readily.
A hundred years ago, there was a very brisk trade in capon roasters in the US, notably in the Northeast. They were much in demand and quoted prices were considered "premium" in their day. Today, caponising is an artisan craft and not much practiced. Since the 1960's, the modern Cornish Cross broiler has all but eliminated the capon, and they are sold in only in a few regional markets in this country. Thereis only one commercial concern, Wapsi Produce, Inc, that handles them. See them here:
Wapsie Capons
In theory, caponising is very simple. In practice, the surgery is risky for the bird - the death rate is high while the caponiser learns his craft. It isn't for the squemish and those who are inclined to try it should have pretty steely nerves. I don't - I have never done it.