  We obtain new regular black hole solutions for an action in 2+1 dimensions
with bilocal Ricci scalar and negative cosmological constant. Besides their
connection to the cosmological constant, these solutions depend on a
fundamental length due to their non-local nature. The effective profile
densities that result from the non-local geometries have quasi-localized
mass/energy since they are finite at the origin and their integration in all
space is convergent. The black holes obtained are free of singularities and
present one, two, or none horizons depending on the values of the involved
parameters. The new solutions can have either an AdS, dS, or even a flat core.
In the case of a de-Sitter core, it could represent a repulsive force coming
from quantum effects. Although the resulting (effective) cosmological constant
is positive near the origin, the classical (naked) counterpart is still
negative thus precluding a cosmological horizon. We investigate the energy
conditions of the effective source and determine the region where exotic energy
should be found. Thermodynamic quantities are also computed. On the one hand,
Gibbs's potential shows that both solutions are globally unstable, as in the
BTZ case. On the other, we show that for small values of the horizon radius the
Hawking temperature is negatively divergent but a finite size remnant can be
defined where $T_H$ crosses zero. At this point, the heat capacity sign changes
from negative to positive, indicating that the black holes are locally stable
while irradiating. Thus, such a quantity, along with $T_H$, presents crucial
differences with the BTZ black hole for small horizon radii where quantum
effects become relevant. Finally, we analyze the bilocal black hole geodesics
and find stable circular orbits for massless and massive particles, another
feature absent in the BTZ case.
