Will my new, unhatched eggs be used if I start to research a new branch?

The very first egg that you complete on each dragon is first reserved for incubation. Once you complete the first egg, every succeeding completion of the egg will be turned into an egg currency which you can use to do the following:

1. Upgrade a Builder's Hut
2. Upgrade the Egg Token Mission Blimp
3. Research

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As an example:

You have Gloomclaw undiscovered and not yet completed. This dragon requires 1,100 egg fragments to become 1 whole egg.

The moment you completed all 1,100 egg fragments, it is then placed to your incubator storage which can then be used to incubate Gloomclaw. After that, once you complete the dragon again (reached 1,100 egg fragments), you will obtain a garnet egg currency which you can now use for upgrading and researching.

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Always remember to double check your parent combination before breeding whenever you plan on focusing in getting an egg currency to avoid misusing your precious egg tokens.