(Abridged) The Edgeworth-Kuiper belt with its presumed dusty debris is a natural reference for extrsolar debris disks. We employ a new algorithm to eliminate the inclination and the distance selection effects in the known TNO populations to derive expected parameters of the "true" EKB. Its estimated mass is M_EKB=0.12 M_earth, which is by a factor of \sim 15 larger than the mass of the EKB objects detected so far. About a half of the total EKB mass is in classical and resonant objects and another half is in scattered ones. Treating the debiased populations of EKB objects as dust parent bodies, we then "generate" their dust disk with our collisional code. Apart from accurate handling of collisions and direct radiation pressure, we include the Poynting-Robertson (P-R) drag, which cannot be ignored for the EKB dust disk. Outside the classical EKB, the radial profile of the optical depth approximately follows tau \sim r^-2 which is roughly intermediate between the slope predicted analytically for collision-dominated (r^-1.5) and transport-dominated (r^-2.5) disks. The cross section-dominating grain size still lies just above the blowout size (\sim 1...2 \microm), as it would without the P-R transport. However, if the EKB were by one order of magnitude less massive, the optical depth profile would fall off as tau \sim r^-3, and the cross section-dominating grain size would shift from \sim 1...2\microm to ~100 \microm. These properties are seen if dust is assumed to be generated only by known TNOs. If the solar system were observed from outside, the thermal emission flux from the EKB dust would be about two orders of magnitude lower than for solar-type stars with the brightest known infrared excesses observed from the same distance. Herschel and other new-generation facilities should reveal extrasolar debris disks nearly as tenuous as the EKB disk. The Herschel/PACS instrument should be able to detect disks at a \sim 1...2M_EKB level.

18 pages, 14 figures, accepted for publication in A&A