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We design and lithographically fabricate two-dimensional preassembled colloidal linkages of custom-shaped, discrete, mobile microscale tiles that are sterically coupled together by lock-and-key sub-tile features, yielding hinge-like bonds between separate tiles. These mobile colloidal linkages, which we call polylithomers, provide top-down, preconfigured, morphologically controllable analogs of fluctuating molecular polymers. We illustrate the versatility of this approach by fabricating and studying curvilinear, branched, bridged-spiral, dendritic, and mesh-like polylithomers having controllable preassembled dimensions, topologies, configurations, intrinsic local curvatures, persistence lengths, and bond extensibilities. By advancing anisotropic particle tracking routines to handle lock-and-key tiles, we measure the dynamic conformational changes of polylithomers caused by Brownian excitations to the monomer scale, revealing markedly large bond extensibilities. Beyond modeling fluctuating semiflexible molecular polymers, polylithomers provide access to unusual polymer morphologies and bonding potentials that have not yet been synthesized through other kinds of assembly methods using either molecular or colloidal monomers.