  It is shown that the Confluent Heun Equation (CHEq) reduces for certain
conditions of the parameters to a particular class of Quasi-Exactly Solvable
models, associated with the Lie algebra $sl (2,{\mathbb R})$. As a consequence
it is possible to find a set of polynomial solutions of this quasi-exactly
solvable version of the CHEq. These finite solutions encompass previously known
polynomial solutions of the Generalized Spheroidal Equation, Razavy Eq.,
Whittaker-Hill Eq., etc. The analysis is applied to obtain and describe special
eigen-functions of the quantum Hamiltonian of two fixed Coulombian centers in
two and three dimensions.
