How do you get Heirs?

You'll need to constantly visit your Consorts in Harem (not random or auto-visit) for a chance to greatly improve your intimacy with them and give birth to Heirs. Like Consorts, they can offer additional boost to specific Viziers improving its performance and power. When they also achieve their fully grown-up stage, you can match them (for Marriage) with other player's heir to earn some sort of shared bonus that will benefit both players.