"Every farmer, every laborer, every fisherman can both read and write — and we think that books instead of being locked up in cupboards, far from the sight of students, should be distributed as widely as possible. The books of our library are therefore
passed from hand to hand without returning to the library shelves perhaps for years."
If they're actual leaflets they shouldn't be registered at all, but there's nothing wrong with registering those very slim softcover children's books. I'd leave them in the same places I leave anything else - playgrounds are a good option, waiting rooms at places where someone might bring children (dentists, pediatricians, hair salons...) or even where they wouldn't (the grownups might like to take the books home for their kids), and of course OBCZs, Little Free Libraries, or other book-swap shelves. If they're really lightweight I wouldn't leave them outside on a windy day unless I could put a rock on top - or could hang them from a tree in a plastic bag - but otherwise I wouldn't see any limits. Heck, it's the books with extreme adult matter that cause more "where can I release this" headaches!
My local supermarket used to have child-sized shopping carts, and another had those carts with a sort of "car" on the front where the kids would sit. I would always have a book or two to leave in one of those places.