What happens during divorce if I buy a house in the course of our marriage, and he didn't contribute anything both for purchase or mortgage.

The short answer is that if it was acquired during the marriage and the source of funding for the purchase / monthly payments came from income earned during the marriage, it is in the pot for division purposes regardless of how title is held. Think about a guy working full time and his wife is a homemaker taking care of the children.... and he purchases a home in his name alone and he makes all of the monthly payments and the down payment from his employment and then takes the position that since title is in his name alone and he made all of the payments and he was the one who worked to support the family, it should be his home alone - wrong!  Here is a legal principle that every family law attorney will tell you about - if you thought he was a bum and did not contribute to the marriage, then you could have divorced him 5 years ago, 4 years ago, etc but you made the decision to stay married to him and there are consequences to your actions - one of which is that an asset was acquired and is subject to division in a divorce.  Now, here is the critical information that you need to focus on. If you have a consultation with a lawyer and he tells you that he thinks that you have a strong shot at keeping the home, free and clear of any claim by your husband in the divorce.... press him to explain to you why and whether his position is supported by the law. My sense is that he will simply tell you that he is hopeful that your husband will simply not want to fight and as a result, you will get to keep it. That though is a very different position than telling you that legally your husband has no claim to share in it. Be wary and make sure that you ask questions and challenge any lawyer telling you simply what you want to hear.