  This paper establishes several upper and lower estimates for the maximal
number of the connected components of the solution sets of monotone affine
vector variational inequalities. Our results give a partial solution to
Question~2 in [N.D. Yen and J.-C. Yao, \textit{Monotone affine vector
variational inequalities}, Optimization 60 (2011), pp. 53--68] and point out
that the number depends not only on the number of the criteria but also on the
number of variables of the vector variational inequality under investigation.
