The fraction of star-forming to quiescent dwarf galaxies

varies from almost infinity in the field to zero in the centers of

rich galaxy clusters. What is causing this pronounced morphology

density relation? What do quiescent dwarf galaxies look like when

studied in detail, and what conclusions can be drawn about their

formation mechanism?  Here we study a nearly magnitude-complete sample

(19 < Mr < 16 mag) of 121 Virgo cluster early types with deep

near-infrared images from the SMAKCED project. We fit two-dimensional

models with optional inner and outer components, as well as bar and

lens components (in 15% of the galaxies), to the galaxy images.  While

a single S\'ersic function may approximate the overall galaxy

structure, it does not entirely capture the light distribution of

two-thirds of our galaxies, for which multicomponent models provide a

better fit. This fraction of complex galaxies shows a strong

dependence on luminosity, being larger for brighter objects. We

analyze the global and component-specific photometric scaling

relations of early-type dwarf galaxies and discuss similarities with

bright early and late types. The dwarfs global galaxy parameters show

scaling relations that are similar to those of bright disk

galaxies. The inner components are mostly fitted with S\'ersic n

values close to 1. At a given magnitude, they are systematically

larger than the bulges of spirals, suggesting that they are not

ordinary bulges. We argue that the multicomponent structures in

early-type dwarfs are mostly a phenomenon inherent to the disks and

may indeed stem from environmental processing.