kol.
anyway an overview of a particular subsystem of the slime farm collection system, which i designed entirely by myself.
so the input to the system is the item elevator, which brings slime balls up to a 2x2x1 region (1 high). so the simplest solution is just to put 4 hoppers there, but that doesn't work because due to the mechanism which stacks many dropped items, the item stacks tend to accumulate only at the north-west hopper, which results in imbalanced distribution.
nor is it sufficient to simply redistribute the contents of that hopper, since the bandwidth of a single hopper is 9k/hour, and the farm produces more than that. so it is necessary to have 4 separate hoppers taking input from the item elevator
the solution (see picture 1) is to have a 2x2 water stream which goes into 4 hoppers, but the stream is controlled by two pistons, which only allows 1 of 2 source blocks to flow, "aiming" the stream so that items prefer 2 of the 4 hoppers at a time.
picture 2: i made use of QC here in order to maximize the amount of glass i could use. notice the outward facing pistons which are essential. note that exactly one of the two pistons is always powered
picture 3: the main meat is here. the whole system is powered by a 12-hopper clock, which activates the zero-tick t-flip-flop circuit using the ability of sticky pistons to drop blocks. the redstone block then powers the pistons.