We present narrowband images and [Nii]lambda 658.3 nm spectra, obtained under sub-arcsec seeing conditions, of the extended nebulae around the symbiotic Miras He 2-147, HM Sge, and V1016 Cyg. The main results of this study are: The nebula around He 2-147 is a ring expanding with a velocity of ~ 100 km s(-1) which is inclined at ~ 55(deg) to the line of sight. The kinematical age of the ring is between 220 and 340 yrs, depending on the adopted distance, and its size is of the order of 10000 a.u. The bulk of the [Nii] core emission of HM Sge is produced in an extended circumbinary region which, along the North-South direction, has a size of 0'' . 4, much larger than the binary orbit. HM Sge possesses a curved, collimated string of knots extending out to a distance of about 9'', with a fainter counterpart on the other side of the central star. We discuss the possibility that it is the result of a fast collimated wind from the white dwarf and (precessing) accretion disc. If so, its age would be ~ 500*Dkpc yrs, where Dkpc is the (poorly known) distance to HM Sge in kpc. The [Nii] core emission of V1016 Cyg is resolved into two blobs separated by 59+/-5 km s(-1) and by 0'' . 40+/-0'' . 06 (extrapolated to P.A.=+80(deg) ), which are identified with the kinematical features found by Solf (cite{S83}) in 1982. We compute an upper limit to their proper motions in the last 15 yrs, and show that they are not ejecta from the 1965 outburst. V1016 Cyg is surrounded by a 20'' elongated nebula, whose major axis is at P.A.=+45(deg) . Along this direction, we find an extended kinematical feature with projected velocities of about +/-30 km s(-1) which extends 3'' from the centre, ending on the SW side in a low-ionization knot. These data provide unique information on the occurrence, geometry and dynamics of ancient mass loss events from these systems, which are likely to be related to unrecorded outbursts of their hot components. We set constraints on the recurrence time between outbursts and the accretion rates of the hot components, using the observed high incidence of nebulae among symbiotic Miras, the observed multiple nebulae, and the maximum observed age of the nebulae. We also discuss the implications of the observations of these nebulae for the theories of formation of aspherical planetary nebulae. Based on observations obtained at the 3.5m NTT telescope of the European Southern Observatory, and at the 2.6m NOT telescope operated on the island of La Palma by NOTSA, in the Spanish Observatorio del Roque de Los Muchachos of the Instituto de Astrofísica de Canarias.