Credits: h_yusaku, FEA 2ch strategy wiki

Opposite gender characters who obtain an “S” support level will marry and their children will join up in paralogues
after a certain point in the game.

The appearance and characteristics of the child who joins is dependant on the mother, although the child’s hair colour will resemble his/her father.

Chrom and Your Avatar

Chrom will always has a daughter named Lucina, in addition to the mother-dependant child. For example, if Chrom marries Sumia, you will get both Lucina and Cynthia.

Similarly, if your Avatar marries, he/she will always have a child named Morgan, in addition to the mother-dependant child (if your Avatar is male). Morgan also has very special properties compared to other children:

• Morgan’s gender is the opposite of your Avatar’s. So if your Avatar is male, Morgan will be female.
• His/her starting class is the same as your Avatar’s partner’s default non-promoted class. If your Avatar’s partner is a Lord, Dancer or Conqueror, Morgan’s starting class defaults to Tactician.
• Morgan’s hair colour resembles your Avatar’s partner.

Characters Who Don’t Bear Children

Anna, Say’ri, Tiki, Flavia, Emmeryn and Aversa don’t have children of their own, but marrying them with your Avatar will produce Morgan.

Children characters can marry each other, but won’t produce offspring. However, they may marry your Avatar and produce Morgan.

Inheritance

Base stats and growth rates are inherited, but these aren’t very important in the long run. Weapons and items are not inherited, since the parents are still around.

Children characters inherit the sum of their parent’s maximum stat modifiers, +1. If your Avatar pairs with a children character, Morgan does not receive the +1 to his/her modifiers.

The children inherit the last active Skill from each of their parents. This can include Skills from gender-specific classes (except Special Dance), so you can have Demoiselle on male children. Chrom’s children are exceptions–his daughter(s) will always learn Aether and his son will always inherit Rightful King (even if Chrom hasn’t learnt either Skill). Skill inheritance occurs at the moment you enter the mission required to recruit the child, so you’ve got plenty of time to play around with the parents’ Skills.

In general, children inherit all the regular class options from both their parents (so a lot of classes if one of their parents is your Avatar), except classes exclusive to the opposite gender. If a class option cannot be inherited due to gender issues, that option will be replaced with another option more appropriate for their gender (see table below). Despite being a Special class, Villager can be inherited by male children and both Taguel and Manakete can be inherited by Morgan.

Classes and Skills obtained from DLC (this includes Skills learned by DLC classes) can not be inherited.

* Even though Wyvern Rider isn’t gender-exclusive

For reference, the character links at the top of this page cover class set and maximum stat inheritance for all possible parents (except for your Avatar who has variable maximum stats). Also covered are all the Skills they can inherit from parents, but can’t obtain by themselves (Unique Inheritable Skills).