  Theories of large extra dimensions (LEDs) such as the Arkani-Hamed,
Dimopoulos & Dvali scenario predict a "true" Planck scale $M_\star$ near the
TeV scale, while the observed $M_{pl}$ is due to the geometric effect of
compact extra dimensions. These theories allow for the creation of primordial
black holes (PBHs) in the early Universe, from the collisional formation and
subsequent accretion of black holes in the high-temperature plasma, leading to
a novel cold dark matter (sub)component. Because of their existence in a
higher-dimensional space, the usual relationship between mass, radius and
temperature is modified, leading to distinct behaviour with respect to their
4-dimensional counterparts. Here, we derive the cosmological creation and
evolution of such PBH candidates, including the greybody factors describing
their evaporation, and obtain limits on LED PBHs from direct observation of
evaporation products, effects on big bang nucleosynthesis, and the cosmic
microwave background angular power spectrum. Our limits cover scenarios of 2 to
6 extra dimensions, and PBH masses ranging from 10 to $10^{21}$ g. We find that
for two extra dimensions, LED PBHs represent a viable dark matter candidate
with a range of possible black hole masses between $10^{17}$ and $10^{23}$ g
depending on the Planck scale and reheating temperature. For $M_\star = 10$
TeV, this corresponds to PBH dark matter with a mass of $M \simeq 10^{21}$ g,
unconstrained by current observations. We further refine and update constraints
on "ordinary" four-dimension black holes.
