Marking or just not housebroken?

My almost 20 month olk jack russell- male- has been neutered... pees in the kitchen- where we have to keep him because we can't trust him run of the house yet. My question when they are marking do they pee a lot or just a little here and there. He has several places he goes- but when he goes.... he goes.. a big puddle. I was thinking that marking would just be a few drops here and there. He pees around the front of his crate and around the legs of the table and another spot just in front of the stove if we leave him alone in the kitchen for any amount of time. He never does it if we are in there?? Do we need to start the house-breaking process over... What do you suggest?