  To regularize the three-body problem, Minlos and Faddeev suggested a
modification of zero-range model, which diminishes interaction at the
triple-collision point. The analysis reveals that this regularization results
in four alternatives depending on the regularization parameter $ \sigma $.
Explicitly, Efimov or Thomas effects remain for $ \sigma < \sigma_c $, the
additional boundary conditions of two types should be imposed at the
triple-collision point for $ \sigma_c \le \sigma < \sigma_e $ and $ \sigma_e <
\sigma < \sigma_r $, and the problem is regularized for $ \sigma \ge \sigma_r
$. Critical values $ \sigma_c < \sigma_e < \sigma_r $ separating different
alternatives are determined both for a two-component three-body system and for
three identical bosons.
