Importance of supervision when potty training: Until your puppy is house trained, he cannot have the full range of the house. He should be supervised at all time. If you cannot supervise him, he should be in a crate or a small (let me say this again, SMALL) puppy safe playpen. You need to be able to see him at all time, so I recommend either having him be tethered to you or section off your house. This way you can get to him quickly and avoid chasing him. Remember, if you did not see the accident happen, you CANNOT do anything about it except clean it up.
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How long can I leave my puppy unsupervised while potty training?
I would not recommend trusting your puppy until they are about 9 months old and have consistently shown that they are potty trained. Around that time, they should be able to hold their urine for about 8 hours, so if planning to be away for longer, arrangements need to be made so your dog has access to use the bathroom. Until then, they need to be supervised or have limited access to your house. I suggest crating your dog until they can wonder around the house on their own. Slowly let them have more and more access to the house until they can control their potty!