I did some looking – from http://www.greenigsociety.org/tailloss.htm
Will my iguana’s tail grow back? Iguanas do not re-grow their tails as quickly or as consistently as some species of geckos, which can drop their tails, run off, and in a month or so have a brand new tail. Tail re-growth in iguanas depends on a few factors. These are the age of the iguana, the health of the iguana, and to a certain extent where the tail was amputated. The younger the iguana, the greater the chance of re-growth. The healthier the iguana, the greater the chance of re-growth. And if the amputation was near a natural breaking point, there is a slightly greater chance of re-growth. The re-growth will never look like a normal iguana tail. It tends to be more club-like than tapered and the scales are not the same as the rest of the scales on your iguana’s body. The scales tend to be smoother than those on the body. The color of the tail also won’t be the same as it was before. It appears that the color of the tail takes on the shade of color where the break occurred. If the break occurred in a dark band of your iguana’s tail, it’s likely that the re-growth will be dark. If it occurred in a light area, chances are the re-growth will be lighter. It also won’t reach the length that an intact tail would. Sometimes, for whatever reason, a young iguana’s tail won’t grow back. On the other hand, an older iguana’s tail might just grow a significant amount. There is no way to predict whether or not there will be any re-growth.
The Panama Adventure 
Can they shed their tails if something grabs it?
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I think so. I’ve seen a couple missing parts of their tails
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I did some looking – from http://www.greenigsociety.org/tailloss.htm
Will my iguana’s tail grow back? Iguanas do not re-grow their tails as quickly or as consistently as some species of geckos, which can drop their tails, run off, and in a month or so have a brand new tail. Tail re-growth in iguanas depends on a few factors. These are the age of the iguana, the health of the iguana, and to a certain extent where the tail was amputated. The younger the iguana, the greater the chance of re-growth. The healthier the iguana, the greater the chance of re-growth. And if the amputation was near a natural breaking point, there is a slightly greater chance of re-growth. The re-growth will never look like a normal iguana tail. It tends to be more club-like than tapered and the scales are not the same as the rest of the scales on your iguana’s body. The scales tend to be smoother than those on the body. The color of the tail also won’t be the same as it was before. It appears that the color of the tail takes on the shade of color where the break occurred. If the break occurred in a dark band of your iguana’s tail, it’s likely that the re-growth will be dark. If it occurred in a light area, chances are the re-growth will be lighter. It also won’t reach the length that an intact tail would. Sometimes, for whatever reason, a young iguana’s tail won’t grow back. On the other hand, an older iguana’s tail might just grow a significant amount. There is no way to predict whether or not there will be any re-growth.
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