Nest Removal for Pigeons
It does sound as though nest removal might be the best outcome for a pest pigeon problem, but in reality, things are very different. The location of pigeon nests is one that the birds will remember for many, many years, which means there's no doubt they'll try to come back at some point. These birds also tend to be a little ... picky ... about the exact places of roosting and nesting spots. They might recognize the nest in its new place, but they won't like it much. In fact, they are more likely to avoid going anywhere near the nest and could abandon it completely.
When the parent pigeons abandon the nest, they kind-of become your responsibility. The pigeon squabs or eggs will either die or not hatch without the parents present, and it won't be pleasant for you to slowly watch a nest full of baby pigeons die in that manner. Even if they were to survive on whatever food source you provided for them, they wouldn't have the parents around to teach them how to do important things, such as flying and finding food. These are not things that you can teach the pigeon youngsters yourself, so you'd be effectively left with a nest of new children. (And no, it's not a very good idea to have pigeon pets.)
What happens if you find a nest of orphaned pigeons?
Firstly, there's a good chance that the pigeon nest isn't actually orphaned at all and the mother will come back for it.
Secondly, you can't disrupt the nest in any way, because this will cause the pigeon parents to abandon the nest even if they hadn't already.
Thirdly, disrupting or moving the nest doesn't actually solve the problem. If the nest is inside your building, you must work out how the parents got in, in the first place. If the nest isn't inside your building, you'll still need to check out the upper levels and other rarely-visited areas of the home, building or property. Pigeons tend to roost somewhere close to where they feed, so if they're feeding close to where your property is, the nest could be actually on it.
Who should I call?
Local pest control organizations and professionals can help with pigeons, although they are likely to offer their services at a cost. In cases such as this — when a nest has been found and it does appear to be orphaned — the youngsters, also known as squabs, will then be put down. They won't have the chance to survive without their mother or father around to feed them, and then teach them how to feed themselves, fly, and build a nest.
Local pigeon rehabilitators are rare, but they do exist. The internet or local phone book can help you to find a professional rehabber in or around your local area.