Cactus : identity and advice

http://tinyurl.com/527qpv http://tinyurl.com/3gvfp6
Apologies in advance, I am a level below beginner when it comes to matters green.
In the photo you will see "mummy" cacti which has many many babies growing. The second photo shows some of last years babies that I removed and replanted. They are growing like a dream.
Some silly questions:
1) Can you identify the type of cactus in the pictures? 2) When is the best time to remove the babies from mummy, what is the best way? 3) I am running out of space - I've given cactus presents to friends and family - what can I do with the new babies?! I'd hate to end up throwing them on the compost :(
All help and advice very appreciated!
Regards Mark
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markemerson

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