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 $ u$ = 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 SPHEREs 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.
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