We have studied the structure of K-pp comprehensively by solving this three-body system in a variational method, starting from the Ansatz that the Lambda (1405) resonance ( Lambda*) is a K(-)p bound state. The structure of K-pp reveals a molecular feature, namely, the K- in Lambda* as an "atomic center" plays a key role in producing strong covalent bonding with the other proton. We point out that strongly bound K nuclear systems are formed by "super strong" nuclear force due to migrating real bosonic particles K a la Heitler-London-Heisenberg, whereas the normal nuclear force is caused by mediating virtual mesons. We have shown that the elementary process, p + p -> K+ + Lambda* + p, which occurs in a short impact parameter and with a large momentum transfer, leads to unusually large self-trapping of Lambda* by the involved proton, since the Lambda*-p system exists as a compact doorway state propagating to K(-)pp.