This anime is about a lot of things, which mostly don't belong together. It's a comedy that includes homelessness, child labour, the yakuza, a girl stranded for years on a desert island and often more seriousness than you'd expect about those. It's about:
1. Hina, a psychic brat who's barely capable of thinking about anything but food.
2. Nitta, her adopted yakuza father, although he got no choice in the matter. He doesn't want to be Hina's dad. He wants to do lots of inappropriate things and get his life back. Sometimes, though, he's a conscientious, nice guy... while at other times he's the worst dad in the world.
3. A girl who talks to coconuts.
4. Blackmailing a thirteen-year-old girl into working in a bar. Also, introducing children of the same age to gambling, rent, employer networking and girlie cabaret clubs.
5. How to be homeless.
6. How to bullshit your family. It probably helps if your sister is a drunkard.
7. Being a yakuza who trusts a documentary-maker to shoot a fly-on-the-wall film about him. (In a show where the cast's full of terrible ideas, this is the worst.)
Sometimes it's serious. It dumps these thirteen-year-old girls into our world as psychic superweapons. Hina can trash an enemy gang by herself. However everyone's completely hopeless in some way or another, which is liable to get played straight. The irresponsible disaster comedy's coming from a base of seriousness. Hina's brainless, shameless and as flexible as an iron girder. Anzu goes from: (a) delinquent to: (b) super-earnest homeless child who learns about community and mutual support, to: (c) someone who's sort of being integrated into society but still has lots to unlearn. Hitomi's the most painful disaster of all, because she's a clever, dutiful girl who who's always done exactly as she should... and yet, in this show, this somehow leads her into completely unsuitable roles, but unlike everyone else she's aware of that.
And then there's Mao. Good grief. She barely intersects with the rest of the show, though.
The yakuza stuff isn't taken too seriously, but in a good way. The show never tries to soft-soap the fact that they're gangsters, but Nitta's also a nice guy, underneath, ish, sort of. By yakuza standards, he's an intellectual. (He collects antiques.) He nearly gets killed by his colleagues at one point, but that was all a misunderstanding (which only makes it funnier). Mostly it's an inappropriate setting where career criminals can worry about good parenting.
The show's command of tone is remarkable. Its characters can make you laugh by doing things like, say, leaving a thirteen-year-old in a bar and forgetting about her. This shouldn't be funny, but it is. It also has a gift for timing its end-of-episode punchlines.
At the same time, though, there's proper character development. Anzu's obviously the ultimate example of this, but even someone like Nitta, for instance, has clear development in his attitude to women-chasing and to Utako. Half-episodes like the homeless community being booted from the park can be dramatically strong. (Like many anime, the show will adapt two manga chapters per episode and will often have a guillotine-like division between the two.) This is an offbeat show. It's too comedy-driven to feel as if it's going anywhere, but there's also a ton of story and development in there. It's as if it's sneaked in. It's wholesome and heartwarming about dreadful things, sometimes to the point of tragedy. (It's tragedy played as comedy by playing it straight as tragedy... but don't worry, she'll be okay.) It includes a detailed, sympathetic look at homelessness in Japan. It's an absurdist comedy. Give it a look.
"Besides, Anzu-chan, if you have honest intent, the gods of horse racing will answer your prayers."