Dividends would be paid to all who held shares (or coins) relevant to how many are owned automatically without having to go through sending every single address their share. There is a possibility these could be newly generated coins as well. Think of what happens in the stock market when shares are added, but split among the entire user base. Take in mind this would be on command so not done steadily like blackcoin or other POS coins.
You can write some code to generate bitcoin transactions automatically. How do you think big corporations pay out their dividends, they have computers which process them automatically.
Dividends are usually paid out depending on profits so a human has to physically tell the computer how much profit has been made.
But I think you aren't really talking about dividends. I think you are talking about some weird process where you give more shares to people who already have shares which serves no real purpose whatsoever.
In real stock markets, when new shares are issued, people have to buy those shares, they aren't just split between existing share holders.
