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We investigate the correspondence between three theories of deformations ofrational surface singularities: de Jong and van Straten's picture deformations,Koll\'ar's P-resolutions, and Pinkham's smoothings of negative weights. Weprovide an explicit method for obtaining, from a given deformation in onetheory, deformations in other theories that parameterize the same irreduciblecomponents of the deformation space of the singularity. We employ thesemi-stable minimal model program significantly for this purpose. We proveKoll\'ar conjecture for various sandwiched surface singularities as anapplication.

Deformations of sandwiched surface singularities and the minimal model program