  Eruptive stars are a class of young stellar objects that show an abrupt
increase in their luminosity. These burst-like episodes are thought to dominate
the stellar accretion process during the class 0/class I stage. We present an
overview of a survey of seven episodically accreting protostars aimed at
studying their potentially complex circumstellar surroundings. The observations
were performed with the instrument SPHERE, mounted at the VLT. We observed the
eruptive stars in $H$-band with the near-infrared imager IRDIS and used the
polarimeter to extract the polarized light scattered from the stars'
surroundings. We produced polarized light images for three FUor objects, Z CMa,
V960 Mon, and FU Ori, and four EXor objects, XZ Tau, UZ Tau, NY Ori, and EX
Lup. We calculated the intrinsic polarization fraction for all the observed
stars. In all systems we registered scattered light from around the primary
star. FU Ori and V960 Mon are surrounded by complex structures including
spiral-like features. In Z CMa, we detected a point source 0.7 arcsec to the
northeast of the primary. Based on the astrometric measurements from archival
Keck/NIRC2 data, we find this source to be a third member of the system.
Further, Z CMa displays an outflow extending thousands of au. Unlike the other
EXor objects in our sample, XZ Tau shows bright, extended scattered light
structures, also associated with an outflow on a scale of hundreds of au. The
other EXors show relatively faint disk-like structures in the immediate
vicinity of the coronagraph. Asymmetric arms were only found around FUor
objects, while faint disks seem to predominantly occur around EXors.
Importantly, for Z CMa the detection of the faint extended structure questions
previous interpretations of the system's dynamic state. The streamer which was
associated with a fly-by object turned out to be part of a huge outflow
extending 6000 au.
