Let's face facts, anime parents have limited options.
1. Find some way to "lose" the kid. Either drop them off at a relatives, get them kidnapped, leave them at an orphanage, have them turned into monsters, etc. A lot just sign any permission slip their teachers hand them and then don't ask questions when the kids disappear at the haunted castle or mysterious back room at the museum. if nothing else hand them a fire breathing rabbit, a backpack, a bus pass, and bid them adieu.
2. Give the kid to a crazy old man or woman who lets them play with soul eating cards and learn dangerous martial arts and magic or play with monsters.
3. Be way too busy to see them most of the time. often calling on Christmas to see how their tript o that island full of monsters went for them and their unsupervised kids. or better yet just send the kid away to bording school to keep themt oo busy to see their parents.
4. Get edited out of the anime
5. Die. At least one of them does this most of the time, much like in family movies liek Disney. Though sometimes they just fake their death.
6. Be completely insane
7. get kidnapped and held hostage... elsewhere.
Am I missing anything?