Dooku can and will groom all of the young whippersnappers. Anakin is getting groomed, he's baby. Asajj is getting groomed, she's the favorite. Maul is getting groomed whether he likes it or not because he is FILTHY and Dooku will not stand for it.
Asajj will also groom Anakin, again because he is baby, and sometimes Dooku is tired, and it's not like anyone can trust MAUL with that.
All three are, for different reasons, disappointed when Anakin is no longer 'carry by mouth' kitten-sized.
There is a special brush for Dooku's coat. Nobody else is allowed to use it (even though Obi-Wan is the one technically using it, on account of having thumbs). He got hissy whenever Obi-Wan tried to use the longhair brush on Asajj or Anakin, and then Asajj got hissy when he tried to get her and Anakin to share one, so he just folded and got three different brushes. It's fine, their respective fur textures are different enough to sort of justify it.
Maul does not need brushing. IDK if he's bald or just a shorthair that can be managed via (Dooku's) grooming, but no brushing needed.
Asajj is very standoffish with most people except Obi-Wan, but she will politely seat herself with Quinlan (Obi-Wan's bestie/situationship/lover/longterm something or other) or Ahsoka (there is a not-insignificant chance that the next thing Obi-Wan adopts will in fact be a human child, not a cat).
Ahsoka, said human (ha) child, is the only person who can manhandle Maul without getting scratched up somehow. Not even Obi-Wan's sure how she manages it. Madness.
(Ahsoka's boyfriend, meanwhile, is not so lucky. Rex has scars from this tiny asshole of a cat.)
This is why Ahsoka gets paid some solid Teenager Cash to stop in and water the plants and feed the cats and clean the litterbox when Obi-Wan has a work conference or something. He doesn't have to worry about getting sued for Legitimate Harm.
Satine no longer comes to Obi-Wan's apartment because Maul is such a fucking nightmare to her specifically, which means that throuple dates with Quinlan have to end in places that are not Obi-Wan's apartment.
(Maul once encountered Bo-Katan and was like... weirdly aloof-but-pleasant around her. Several people tried to convince her to take him on Obi-Wan's behalf and failed, in part because this was discovered by way of Bo-Katan preventing the cat in question from trying to enact his name on Satine.)
Anakin will hide in the hood of Ahsoka's jacket to try and 'sneakily' hitch a ride to the outside world and he gives both her and Obi-Wan the biggest sad eyes when they inevitably fish him out. He does not realize they were humoring him until it was time to leave. He's not that light.
Dooku's favorite person, after Obi-Wan (and Asajj, who is a cat), is the elderly neighbor, Jocasta.
Asajj once escaped to a feral colony for like a week and then came back home and immediately went to the grooming supplies like 'listen, the murder girls out there are great, but I need a cleaning, now.' And that's how Obi-Wan ended up with a bunch of feral Nightsister cats occasionally yowling at his window to get Asajj and Maul to come out and join them in various kitty crimes.