  By means of a multimass isotropic and spherical model that includes the
self-consistent treatment of a central intermediate-mass black hole (IMBH), the
influence of this black hole on the morphological and physical properties of
globular clusters is investigated. In agreement with recent numerical studies,
it is found that a cluster (with mass M) hosting an IMBH (with mass M_BH)
shows, outside the region of gravitational influence of the black hole, a
core-like profile resembling a King profile with concentration c < 2, although
with a slightly steeper behaviour in the core region. In particular, the core
logarithmic slope is s < 0.25 for reasonably low IMBH masses (M_BH < M/100),
and c decreases monotonically with M_BH. Completely power-law density profiles
(similar to, for example, those of collapsed clusters) are admitted only in the
presence of a black hole with an unrealistic M_BH > M. The mass range estimate
12s - 4.8 < log (M_BH/M)< -1.1c - 0.69, depending on the morphological
parameters, is deduced by considering a wide range of models. Applying this
estimate to a set of 39 globular clusters, it is found that NGC 2808, NGC 6388,
M80, M13, M62, M54 and G1 (in M31) probably host an IMBH. For them, the scaling
laws M_BH ~ 0.09(M/M_sol)^{0.7} M_sol and M_BH ~ 50[sigma/ (km s^-1)]^{1.2}
M_sol are identified from weighted least-squares fits. An important result of
this 'collective' study is that a strong correlation exists between the
presence of an extreme blue horizontal branch and the presence of an IMBH. In
particular, the presence of a central IMBH in M13 and NGC 6388 could explain
why these clusters possess extreme horizontal-branch stars, in contrast to
their 'second parameter' counterparts M3 and 47 Tuc.
