Reward of esaal-e-thawaab distributed among the marhooms

When a person reads Surah Yaseen once, he gets the reward of reading the Quraan 10 times. If for example he makes the intention of isaale-thawaab for 10 people in his family when reading the surah, will they each receive the reward of 1 Quraan each, or 10 Quraans each? As in is the reward divided amongst them or each person gets the full reward?

So when making intentions as well for isaale-thawaab, is there a difference between saying "all the marhooms" or specifically mentioning a person's name that you want the reward to be sent to?