When we are out downrigging when the first fish hits your rod it's your fish, when the 2nd fish hits if it's on your rod the first guy to it ( not including the guy who'd rod it is ) gets the fish until everyone has a fish. After that from then on, your rod your fish. Our rule in tourneys is any money prize, everyone on the boat shares the amount equally, but if the prize is an item ( rod, reel, outboard etc. ) then it's your prize.
When out for Smallmouth, Walleye etc if your, lets say indisposed, anyone can grab the rod and your in charge of their rod until the fish is landed.