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Young dogs often seem to urinate more than they drink; however, they don't assuming they are normal active pups. If they actually drank more than they urinated, they would dehydrate rapidly.
Many puppies do not have full ability to concentrate and hold urine for more than a couple of hours until they are 6-12 months old.
Crate training is the easiest way to teach pups to not urinate in the house. The puppies are kept in a crate and taken directly to where they are suppose to urinate when let out. After urinating, they can be allowed to interact for a while before again being let out to urinate. They should be allowed to urinate every several (2-4 hours) until they have shown that they can hold it longer.
At night, taking water away about 2 hours before the last outing and then crating them should help teach them to wait until morning.
Many puppies will do submissive urination and this is often confused with normal urination. They urinate when around other dogs and people who are higher in rank and will urinate if scolded.
Are you using a crate? How much are you limiting water consumption? What type of training regime are you using?
Let me know if you have follow up questions, if my comments have helped. If not, please give me more information on what system you are using to house train the pups.