Who owns the home between the two brothers?

The home is owned by both brothers equally, however, unless one of the brothers removes the home from joint tenancy (by deeding his interest to himself as a tenant in common with the other brother), the surviving brother will become the sole owner, after the first brother dies. The brother that paid off the home or paid for repairs, taxes and insurance (in the name of both brothers) does not get any credit for those payments, except to the extent that they exceed the fair market rental value of the home. If the brother in possession made improvements (as opposed to repairs) that brother is entitled to a credit to the extent of the increased value attributable to those improvements. The resolution of the joint ownership issues between the brothers is addressed in California under the law of Partition.

Generally both brothers still own the house and their wives may have dower rights.... unless the occupation was adverse and without permission...e.g., if the one brother who lives there has claimed he owned it adversely.. e.g., against the other brothers wishes, then he may own it pursuant to the doctrine of "adverse possession".

They both own the house. Depending on what the deal was, one brother may owe the other brother something. If they can't work it out between them, they should consult with an attorney to sort out, if possible, who owes whom what.

If brothers still on deed as joint tenants, they own home jointly.