The behavior of splitters looks simple at first glance. But they are not that simple. Splitters have an astonishing amount of uses.
splitters have two input-belt-sides and two output-belt-sides on which you can connect any belt or underground belt
splitters don't shuffle the lanes on the belts; items on the left input belt lane don't change the side to the right lane (and vice versa).
Splitting
if two output-belts are connected, then every input-item is put alternated on one of the two output-belts. Or in other words: it is guaranteed, that the inputed items are output in a ratio of 50% on each belt.
if one of the output belt lanes are full, then it tries to output on the other output belt. This is useful to fill belts.
JoiningFile:T&T Belt04.jpgFeeding from side is only a good use, if you want to make a queue - e. g. for mines, some output-bufferFile:T&T Belt03.jpgBetter: The capacity of the output belt is fully used.
splitters can be used to join two belts into one. This has a much higher throughput than only side-inserting.
as with splitting, the belt lanes aren't mixed up.
Use faster splitter if you want to feed into a faster belt, because otherwise your splitter is the bottleneck!
Expert
Special behavior
Splitters/Priority: right input is only taken to fill gaps in the left input.
Splitters/Wormhole Trick: items disappears on input side and dive up on output side, "jumping" over half a tile, which is when stacked up in a line of splitters like a wormhole. (Completely untested, just waked up and known that it must be like that - ssilk)