  We present a search for luminous, long-duration ambiguous nuclear transients
(ANTs) similar to the unprecedented discovery of the extreme, ambiguous event
AT2021lwx with a $>150$ d rise time and luminosity $10^{45.7}$ erg s$^{-1}$. We
use the Lasair transient broker to search Zwicky Transient Facility (ZTF) data
for transients lasting more than one year and exhibiting smooth declines. Our
search returns 59 events, seven of which we classify as ANTs assumed to be
driven by accretion onto supermassive black holes. We propose the remaining 52
are stochastic variability from regular supermassive black hole accretion
rather than distinct transients. We supplement the seven ANTs with three
nuclear transients in ZTF that fail the light curve selection but have clear
single flares and spectra that do not resemble typical AGN. All but one of
these 10 ANTs have a mid-infrared flare from an assumed dust echo, implying the
ubiquity of dust around the black holes giving rise to ANTs. No events are more
luminous than AT2021lwx, but one (ZTF19aamrjar) has twice the duration and a
higher integrated energy release. On the other extreme, ZTF20abodaps reaches a
luminosity close to AT2021lwx with a rise time $<20$ d and that fades smoothly
in $>600$ d. We define a portion of rise-time versus flare amplitude space that
selects ANTs with $\sim50$ per cent purity against variable active galactic
nuclei. We calculate a volumetric rate of $\gtrsim 3\times10^{-11}$ Mpc$^{-1}$
yr$^{-1}$, consistent with the events being caused by tidal disruptions of
intermediate and high-mass stars.
