You can always use sell province (with the cossacks dlc Grant province) to hand provinces over to your subjects. They will always take provinces, which are their cores. But they will pretty much take any province as long they have 0% overextrension and the offered province keeps their realm contingous. They will then immediately start coring the province and after that's done you can offer them a new province.
The second option opens with the art of war dlc(or cossacks works for this as well). You can now transfer occupation of any province to any ally in a war. Handing over occupation to a vassal this way will grant the province to your vassal in the peace deal.
Keep in mnid, you almost always have to do this manually, as any province occupied by a vassal automatically conuts as occupied by you unless the province is a core of your vassal.
On top of that, there are plenty of reasons to hand provinces to vassals. Powerful enough vassals can handle internal strife and smaller conflicts by themselves without your interaction. Especially a world conquest game is made much more manageable this way.
Diplomatic points are usually less valuable than admin, so having a vassal core provinces for you and then annex him is often a good idea. Feeding vassals has been a strategy so strong, it received numerous nerfs over the many patches the game has seen.