Let us explain ... in a declaration filed in the couple's nasty custody battle -- Paul cops to packing heat for the last 9 years (as alleged by Adrienne Maloof in a previous statement) ... but is ADAMANT he has good reason to think his family is at risk and therefore needs a gun.

Paul says that since his sons are the sole heirs to a BILLION-DOLLAR estate they're an easy target. But there's more ...

Paul says he and his estranged wife -- whose family owns the Kings -- have been inundated with threats over the last year ... all because they're contemplating moving the Kings out of Sacramento to Virginia City -- a move that has Kings fans up in arms.