  The bubbles that nucleated during slow-roll inflation can be supercritical,
i.e. their radii are larger than the Hubble horizon of de Sitter spacetime
inside the bubble (an inflating baby universe inside it), and thus naturally
develop to the supermassive primordial black holes (SMPBHs) with a multi-peaks
mass function. In this paper, we further investigate relevant phenomenology.
After slow-roll inflation ended, the bubbles may be not only supercritical, but
also subcritical. It is showed that it seems unlikely for the subcritical
bubbles to collapse to SMPBHs. Theoretically, however, before they collapsed
such bubbles might have a probability of up-tunnelling to the supercritical
ones and thus contribute to SMPBHs. We present a mechanism for the origin of
initial clustering of SMPBHs, which can significantly magnify the merger rate
of SMPBH binaries, and show the possibility that the merging of such SMPBH
binaries explains recent NANOGrav signal.
