No. Assets acquired after the separation are not marital property to be distributed, but the court will consider non-marital assets in determining the manner in which the marital assets will be distributed. It is one of the factors. However, the funds that you received would be income for support purposes.
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It's impossible to answer accurately without more information.
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Highly doubtful since it was during the separation and although you say not from a Will, it sounds like an inheritance to me, sort of anyway.
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If from the date his name was put on the house and the date you separated from your spouse the value of the house increased, then you may be entitled to a portion of the increase. Also, if marital funds were used to purchase the house or maintain the value of the house then you could seek a credit for contribution towards the equity of the asset even though it may not have been a marital asset.
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