  Nearly a hundred progenitor-less, thin stellar streams have been discovered
in the Milky Way, thanks to Gaia and related surveys. Most streams are believed
to have formed from star clusters and it was recently proposed that extended
star clusters -- rich in stellar-mass black holes (BHs) -- are efficient in
creating streams. To understand the nature of stream progenitors better, we
quantify the differences between streams originating from star clusters with
and without BHs using direct $N$-body models and a new model for the density
profiles of streams based on time-dependent escape rates from clusters. The QSG
(Quantifying Stream Growth) model facilitates the rapid exploration of
parameter space and provides an analytic framework to understand the impact of
different star cluster properties and escape conditions on the structure of
streams. Using these models it is found that, compared to streams from BH-free
clusters on the same orbit, streams of BH-rich clusters: (1) are approximately
five times more massive; (2) have a peak density three times closer to the
cluster 1 Gyr post-dissolution (for orbits of Galactocentric radius > 10 kpc),
and (3) have narrower peaks and more extended wings in their density profile.
We discuss other observable stream properties that are affected by the presence
of BHs in their progenitor cluster, namely the width of the stream, its radial
offset from the orbit, and the properties of the gap at the progenitor's
location. Our results provide a step towards using stellar streams to constrain
the BH content of dissolved (globular) star clusters.
