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Enormous Ly$\alpha$ nebulae (ELANe) around quasars have provided uniqueinsights into the formation of massive galaxies and their associations withsuper-massive black holes since their discovery. However, their detectionremains highly limited. This paper introduces a systematic search for extendedLy$\alpha$ emission around 8683 quasars at $z=$2.34-3.00 using a simple butvery effective broad-band $gri$ selection based on the Third Public DataRelease of the Hyper Suprime-Cam Subaru Strategic Program. Although thebroad-band selection detects only bright Ly$\alpha$ emission($\gtrsim1\times10^{-17}$ erg~s$^{-1}$cm$^{-2}$arcsec$^{-2}$) compared withnarrow-band imaging and integral field spectroscopy, we can apply this methodto far more sources than such common approaches. We first generated continuum$g$-band images without contributions from Ly$\alpha$ emission for host andsatellite galaxies using $r$- and $i$-bands. Then, we established Ly$\alpha$maps by subtracting them from observed $g$-band images with Ly$\alpha$emissions. Consequently, we discovered extended Ly$\alpha$ emission (withmasked area $>40$ arcsec$^2$) for 7 and 32 out of 366 and 8317 quasars in theDeep and Ultra-deep (35 deg$^2$) and Wide (890 deg$^2$) layers, parts of whichmay be potential candidates of ELANe. However, none of them seem to beequivalent to the largest ELANe ever found. We detected higher fractions ofquasars with large nebulae around more luminous or radio-loud quasars,supporting previous results. Future applications to the forthcoming big datafrom the Vera C. Rubin Observatory will help us detect more promisingcandidates. The source catalogue and obtained Ly$\alpha$ properties for all thequasar targets are accessible as online material.

Search for extended Lyman-$\alpha$ emission around 9k quasars at z=2-3