Abandoning is an action available to unfrozen hatchlings and eggs. This can be used if you no longer want the dragon in question; you can then abandon it, and it will go to the Abandoned Page (AP). Here, another user can pick it up. Eggs from multi-clutches will be auto-abandoned on the hour, unless you pick one, in which every one except the one that was chosen will be abandoned.
Eggs and hatchlings abandoned gain a day the first time they're abandoned. However, this time can not exceed 7 days.
If you accidentally click a egg from the main cave which you do not want, you can abandon it, but you need to wait five hours. This is to make the five-hour wait more desirable (as Killing an egg still counts on your scroll as a live one for a day) and prevent people from taking unwanted commons in the main cave, and simply abandoning them into the AP. However, there is no such restriction for eggs picked up on the AP, or bred eggs.
If the AP exceeds four lines, it will block the cave, meaning that no eggs from the main cave can be picked up until it goes down to four lines. This will be accompanied by the description: "Near the entrance to the cave, there is a huge pile of abandoned eggs. If you don't want the dragons inside to die, you can take one of those instead."
After Habitats were added to the cave, the cave block description turned into: "As you set off toward the (habitat you are travelling to), you see a massive pile of eggs. You decide that there are plenty of eggs there, and travelling is unnecessary."