Sort of... both? I mean, they're pretty obviously gifts, but they do just kinda... pop up outta nowhere.

It's not like when, say, one of your Pokemon lays eggs or something. Most of the time whatever hatches won't remotely belong to any species you already own.

But, uh... hm. Tryin' to think of an example that wouldn't involve a shitton of backstory. S'tough.