This is an interesting article about Amazon's delivery network, which is now the 4th largest in the United States. Here are the numbers (most of which are as of 2019):
Since 2014, Amazon has spent $39 billion building out its delivery network. When you add in warehouses and airplanes, this number increases to about $60 billion. As of 2019, Amazon leased 97% of its fulfillment and data center spaces.
Amazon is becoming increasingly vertically integrated. Last year, Amazon delivered about 58% of the 4.5 billion parcels that it shipped to US consumers. This represents about 22% of all online retail deliveries.
Outside of the US, Amazon still handles close to 50% of its own order deliveries. By 2025, Bank of America Global Research is predicting that Amazon could grow to handle somewhere between 38% and 49% of all online order deliveries in the US.
Amazon is the 4th largest in terms of US package deliveries (2019), behind FedEx, UPS, and USPS (in that order).
Amazon's fulfillment network roughly entails: receiving centers -> fulfillment centers -> sortation centers -> last-mile delivery stations. It's a hub and spoke system with the physical real estate naturally getting smaller as you get closer to the end destination. For a lot more information on their network, click here.