Despite popular belief, most Amazon facilities do NOT use kiva robots. The fulfillment center would have to be completely rebuilt on the inside to accommodate them. Heck, even some new facilities still don't use them. I work over at Amazon in one of their largest fulfillment centers in the USA. To answer your question regarding where a tote is sent in the facility is simple. During each shift, there are any number of queues open (usually about 5). When receiving an item from DA, we will scan an item into a tote and the computer determines, based on the size of the items, where in the facility it needs to go (library, or library deep). Aside from a few exceptions, most items are randomly stowed. The stowers all have a rate, and because of that, will find whatever space fits their needs. Pallet mass (items with a lot of the same quantity to fill a pallet) is checked regularly and pulled from the regular shelves and sent to a sorting area (at least that's what they started doing at my FC) where it can be stowed somewhere in "pallet land." Try not to think too much into where items are stowed, it is pretty much a clusterf*ck across the FC.