On the limit zero distribution of Hermite–Padé polynomials for a pair of functions which form an Angelesco system

It is discussed in the talk the problem of limit zero distribution of type I Hermite–Padé polynomials for the collection of three functions $[1,f_1,f_2]$ when
$$ f_1(z):=\frac1{\sqrt{(z-a_1)(z-b_1)}}, \quad f_2(z):=\frac1{\sqrt{(z-a_2)(z-b_2)}} $$
and under the assumption that $\{a_1,b_1\}\cap\{a_2,b_2\}=\varnothing$.