  The immediate vicinity of T Tauri was observed with the new high-contrast
imaging instrument SPHERE at the VLT to resolve remaining mysteries of the
system, such as the putative small edge-on disk around T Tauri Sa, and the
assignment of the complex outflow patterns to the individual stars. We used
SPHERE IRDIS narrow-band classical imaging in Pa$\beta$, Br$\gamma$, and the
$\nu$ = 1-0 S(1) line of H$_2$, as well as in the nearby continua to obtain
high spatial resolution and high contrast images over the NIR spectral range.
Line maps were created by subtracting the nearby continuum. We also
re--analyzed coronagraphic data taken with SPHERE's integral field spectrograph
in $J$- and $H$-band with the goal to obtain a precise extinction estimate to T
Tauri Sb, and to verify the recently reported claim of another stellar or
substellar object in the system. A previously unknown coiling structure is
observed southwest of the stars in reflected light, which points to the
vicinity of T Tauri N. We map the circumbinary emission from T Tauri S in $J$-
and $H$-band scattered light for the first time, showing a morphology which
differs significantly from that observed in $K$-band. H$_2$ emission is found
southwest of the stars, near the coiling structure. We also detect the H$_2$
emitting region T Tauri NW. The motion of T Tauri NW with respect to T Tauri N
and S between previous images and our 2014 data, provides strong evidence that
the Southeast-Northwest outflow triggering T Tauri NW is likely to be
associated with T Tauri S. We further present accurate relative photometry of
the stars, confirming that T Tauri Sa is brightening again. Our analysis rules
out the presence of the recently proposed companion to T Tauri N with high
confidence.
