Once you are convicted of a felony it is your responsibility not to be in violation of any other laws based upon your conviction. As such, any firearms/ammo in your possession after the conviction may be seized and you could face state and or federal charges.
There is no uniform means that courts or LE use to recover FAs after conviction. ATF generally will not charge or seize the FAs if they are turned over or sold to an FFL prior to the conviction or immediately after. Title II FAs have special limitations and would have to go to a class III dealer.
You could dispose of your FAs prior to your conviction to whomever you want if they are not also prohibited. However, after conviction LE may just seize the FAs if something is not worked out with the courts for disposition. For those thinking they will give them to their wife or husband, this may be viable if they can lock them away someplace the prohibited individual does not have access. However, constructive possession will put you in prison just as sure as actual possession. Do not confuse "possession" or "ability to possess" with ownership.
Once had a situation where a felon and non-felon had a FA in vehicle between seat. Driver who was not felon admitted FA was his and had sale paperwork. Passenger stated that he knew it was there within his reach, that his prints would be on FA because he had handled it . He is now back in prison for possessing a FA.
Bottom line is that there is no uniform process, but you become prohibited immediately upon conviction. This is something that must be discussed with your lawyer prior to the final conviction.