Why do NEB adapters have non-complementary sequence? I am making some infographics of different library prep types and noticed something weird about NEB's Ultra II adapters. 

Molecule 1 is the desired product of the adapter ligation step. * indicates a phosphorothioate bond and - indicates a normal bond. | indicates complementary sequence through hydrogen bonding.

Molecule 2 is the product after treatment with the USER enzyme.

Molecule 3 is the result of melting molecule 2 and hybridizing the NEBNext Universal PCR Primer for Illumina.

My question is: Why does Molecule 3 have a large non-complementary region on the 3' end of the original molecule? Is that just to force Molecule 1 to have an open loop conformation so that the USER enzyme can access it better? Or maybe it is something to do with PCR kinetics?

I understand that PCR synthesizes in the 5'-&gt;3' direction, so Molecule 3 only forms with the original adapter-ligated molecules before PCR.
The original point of the non-complementary sequence is to allow formation of a Y-adapter after USER treatment, since that's what's needed for the Illumina chemistry to work. In reality the bottom strand may not be there in step 3, since USER has already digested one strand (creating the hairpin in step 2) and size selection has been performed. Regardless, it'll get removed once cluster formation is performed.