Few things

[12345]

I want to know how to do that the adoptables can be adopt only one time and user must have only one adoptables. So if user adopt pet then he cant adopt another one and other members can adopt this pet. Im little confuse in this new script:P

[BMR777]

When making the new adoptable, set "When can this adoptable be adopted?" equal to "Only when the following conditions are met".

Then find the "The user does not have more than X of this type of adoptable" condition and check the checkbox. Then in the box in the line put the maximum number of this type of adoptable this user can adopt, so in your case you would put a 1 so any given user can only adopt 1 of this type of adoptable. :)