At first they are Eggs which then hatch into Hatchlings (or first stage hatchlings). These hatchlings then turn into Mature Hatchlings (or second stage hatchlings) and finally grow into their Adult form. There are no limits to how many dragons you can keep on your scroll but there is a limit to how many eggs and unfrozen hatchlings you can have at one time.
The base limit is four eggs and eight hatchlings. This changes with the increasing amount of dragons on a user's scroll and their following trophy level:
|1 - 50|
|→||No badge||4 eggs-12 total|
|51 - 200 dragons||→|
|5 eggs-15 total|
|201 - 500 dragons||→|
|6 eggs-18 total|
|7 eggs-21 total|
The first number is how many eggs you may have at one time. The second number refers to the total number of growing dragons you can have. This means you could have (with no trophy, as an example): 4 eggs and 8 hatchlings or 3 eggs and 9 hatchlings or 2 eggs and 10 hatchlings or 1 egg and 11 hatchlings or 0 eggs and 12 hatchlings. If you have 4 eggs, you can still hunt for hatchlings until you've hit 12 total growing things.
The number of living creatures you must have to acquire each trophy level needs to be reached and kept for the increase in the egg/hatchling to stay that way. For example, when you get 501 creatures and can have seven eggs and 21 total growing things on your scroll, if you abandon/release/kill one, your gold trophy will (eventually) become silver, and your limit will be six eggs and 18 total again.
This limit can be taken up by dragons grabbed from the cave, the AP (abandoned page) or bred from your own scroll. There is no "secret" or "extra" slot available anymore. The egg limit posted here is the full egg limit available to you.
Previously, there was no benefit to badges, and you could have 4 eggs/8 total. Also, you could breed a fifth egg making it 5 eggs/9 total.