We describe the physical and orbital properties of C/2011 W3. After surviving perihelion, the comet underwent major changes (permanent loss of nuclear condensation, formation of spine tail). The process of disintegration culminated with an outburst on December 17.6 (T+1.6 d) and this delayed response is inconsistent with the rubble pile model. Probable cause was thermal stress from the heat pulse into the nucleus after perihelion, which could also produce fragmentation of sungrazers far from the Sun. The spine tail was a synchronic feature, made up of dust released at <30 m/s. Since the nucleus would have been located on the synchrone, we computed the astrometric positions of the missing nucleus as the coordinates of the points of intersection of the spine tails axis with lines of forced orbital-period variation, derived from orbital solutions based on preperihelion astrometry from the ground. The resulting osculating orbital period was 698+/-2 years, which proves that C/2011 W3 is the first major member of the predicted new, 21st-century cluster of bright Kreutz-system sungrazers. The spine tails tip contained dust 1-2 mm in diameter. The bizarre appearance of the dust tail in images taken hours after perihelion with coronagraphs on SOHO and STEREO is readily understood. The disconnection of the comets head from the preperihelion tail and the apparent activity attenuation near perihelion are both caused by sublimation of all dust at heliocentric distances smaller than ~1.8 solar radii. The tails brightness is strongly affected by forward scattering of sunlight by dust. The longest-imaged grains had a radiation-pressure parameter beta ~ 0.6, probably submicron-sized silicate grains. The place of C/2011 W3 within the hierarchy of the Kreutz system and its genealogy via a 14th century parent suggest that it is indirectly related to the celebrated sungrazer X/1106 C1.