The true number of ultramassive black holes
Natarajan & Treister 2008, when exploring the mass distribution of very massive black holes, determined from x-ray emissions of populations of active galactic nuclei (AGN) that over cosmological distances, the mean ultramassive black hole density should be at least $\sim3\times10^{-6}$ per cubic megaparsec. If we simply multiple this by your desired volume, we find that a sphere 1 billion light-years in radius should host
$$N=3\times10^{-6}\;\text{Mpc}^{-3}\times\frac{4\pi}{3}(10^6\;\text{light-years})^3\approx360\;\text{UMBHs}$$
This is two or three orders of magnitude higher than Nip Dip's estimate. Note that UMBHs are expected to be rarer in the local universe, i.e. at lower redshifts and much closer to the Milky Way than gigaparsec distances. Locally, the authors derive a density of $\sim7\times10^{-7}$ per cubic megaparsec.
I should also note that the authors describe their density as a "conservative" estimate based on predictions of supermassive black hole accretion rates. On the other hand, it's possible that they overestimated the behavior of high-mass UMBHs, but they claim that this is unlikely.
The number of ultramassive black holes on your map
Now, how many UMBHs should you include on your map? Well, it could be all of them, if you want. An omnipotent civilization capable of traveling far enough to need such a big map might very well have found and mapped all of these ultramassive black holes. On the other hand, keep in mind that this encompasses an area 2 billion light-years in diameter. That's a lot of space! In reality, it's unlikely that the mapmakers will have found all of them. So you have some leeway; you could put only 100 or 200, and make it clear that the map only includes known UMBHs.
The distribution of ultramassive black hole masses
It seems that SMBH and UMBH masses follows a double power law. The point where the mass distribution breaks from one of those power laws to the other appears to happen around a mass of $M_{\text{BH}}\approx10^{8.5}$, at which point it dips sharply. Here's a plot from Natarajan & Treister, showing the quantity $M_{\text{BH}}\frac{dN}{dM_{\text{BH}}}$ as a function of black hole mass, with four different curves representing the distribution from galactic velocity distributions (solid line) and three different values of accretion efficiency (dotted lines, $\epsilon=0.1, 0.05, 0.5$):
I did a little bit of playing around, and eyeballed a fit to a double power law distribution over the entire mass range the authors considered ($10^6M_{\odot}<M_{\text{BH}}<10^{10}M_{\odot}$). The result looks like
$$M_{\text{BH}}\frac{dN}{dM_{\text{BH}}}=\frac{1}{\left(f_{\text{low}}(M_{\text{BH}})^{-1/\alpha}+f_{\text{high}}(M_{\text{BH}})^{-1/\alpha}\right)^{\alpha}}$$
where
$$f_{\text{low}}(M_{\text{BH}})=0.03\left(\frac{M_{\text{BH}}}{10^6M_{\odot}}\right)^{-0.44},\quad f_{\text{high}}(M_{\text{BH}})=10^{-8}\left(\frac{M_{\text{BH}}}{10^{9.78}M_{\odot}}\right)^{-9}$$
and $\alpha=4$.
From this, you can find $\frac{dN}{dM_{\text{BH}}}$ and then numerically integrate to find the fraction of UMBHs that lie in a given range.
Miscellaneous notes
There are a couple of other points I wanted to mention.
- Supermassive black holes never result from the collapse of a single star. Astronomers are divided between the top-down (the collapse of a very massive primordial cloud) and bottom-up (the coalescence of smaller black holes) models, but even in the early universe, you couldn't find stars a million times the mass of the Sun!
- I'd be surprised if there are many cases where a galactic nucleus is dominated by emission not caused by the central supermassive black hole. LINERs may be a counterexample, if the intense emission is due to star formation, but that would presumably be an edge case.
