This is probably the answer to your question:
https://en.bitcoin.it/wiki/Change
But, I'm not sure because I don't know what POS stands for, and I don't know what "split systematically" means, and I don't know what "calculates stake" means.
I'm just doing the best to guess what you're trying to ask, since you asked about "splitting" and transactions that has "2" of something.
Sorry for my English, it is not my first language.
Systematically mean for me all time, calculates stake mean for me calculates POS interest stake.
So when certain wallet using POS calculates interest stake ie: 10% yearly. The wallet select a transaction. Calculate the interest. Add it to the transaction. Then split the transaction in two equal parts, if the level of transaction is sup to 2 to create 2 different new transactions.
This has for effect to multiply the number of transaction in your wallet and because when you are staking so you are not supposed to touch any of your transaction.... The result is:
when you finally want to transfer an important amount of coin you get a failure because too many transaction occurred. That a real problem actually in numerous wallet using POS.
I have a basic understanding of TI but imagine when you address people who are not immersed into TI.....