Axolotls as pets?

First and foremost to those who are not familiar with axolotls. Axolotls are a species of salamanders which do not evolve past the larvae stage. In the wild they are considered rare and only to be found in Mexico. However they do thrive well in captivity and are nowadays mostly found as pets.
Well, this does seem to be a weird choice of pet does'n it? I first came across axolotls when I heard of a biology student keeping one as a pet.
A few weeks later my partner was off to the pet shop in order to buy some catfood and fishfood. Little did I know that he would bring home 4 axolotls. Of course they were not meant as petfood. At first I was a bit cross at him because how had he thought he would keep them and where would he keep them? It was a hot summer day and from what I had learned I gathered axolotls had to be kept in a aquarium/ fishtank at a temperature of 12 to 17 degrees Celcius. As a result the axolotls got a new home in the basement of the house. Much to my surprise they seemed to thrive very well. Well they may even thrive a little bit too well at the moment. November last year, after changing the water of the tank, my partner discovered the axolotls had given birth to 13 babies! Up until now all of the offspring and parents are doing very well. They have grown a lot and resemble their parents more and more.
At this point I am asking myself whether anyone here has ever heard of someone keeping axolotls. The biology student that I mentioned does not keep axolotls anymore. His axolotl has died. If anyone is familiar with axolotls here, could you tell me if any of you has had baby axolotls and did you keep them or did you give them to someone else?
For your information: I am in Belgium, so are the axolotls. It is legal to keep them in Belgium.

The fact that your axolotls have given birth proves that you are keeping them in good conditions. If you don't want to keep all of the young ones I think you should contact the pet shop where the parent axolotls came from and see if the owner is interested in purchasing some of their offspring to sell.

I have never heard of them being kept as pets, but I have seen captive axolotls in zoos and aquariums. They are fascinating little creatures. As long as they are bred in captivity and not taken from the wild I can see no problem with having them as pets.

First of all let me thank you for your response.
I had considered asking the petshop whether they would be interested to sell some of the offspring in the shop. One of the employees there keeps axolotls himself and gave us good advice when we first noticed the little ones. I would feel fine with leaving the babies there. I am sure they would be taken good care of.
Then and again, the petshop is part of a large chain of petshops here in Belgium and I do wonder whether it would be the employee's call to accept our axolotls' offspring. I do not know about the company policy.
However I will ask him the next time we go there, because the little ones are getting bigger all the time and I would not want to experience the offspring having offspring of their own.
I guess the prospect of having even more offspring has made me realize that contacting the petshop is the best idea.