To whom does the court allot the family home after the divorce?

There is no stock answer. Each case is different. It depends on many factors, and you gave no info.

Depends. It varies by state and what your situation is.   My brother just got a divorce and his wife got the house, 2 of the cars AND their cottage.  She's never worked a day in her life and has never contributed to the mortgage, utilities, nothing.   She's a thorn in my side.

If you're fighting over it, it usually is awarded to the one who has custody of the children; if you have no children, then you'll have to sell it and split the profit generally speaking.

We have Family Law, with specific guidelines that determines who gets custody of children, division of community property, etc in the event of divorce.  Gone is the day when everything automatically went to the woman because she was PRESUMED to be spotless and perfect: now we have a much fairer code of law but it is lengthy, is a specific legal specialty, and a separate degree is required to practice that exacting branch of law.

French law now flirts with Sharia abuses, where in the case of legal separation the man gets everything.  Mexican law suffers the age old abuse where the woman still gets everything.  American Statute is much fairer than either.