Excitons in parabolically confined planar quantum dots with a transverse magnetic field have been studied in various model systems. The correlations between e-h, e-e, and h-h have been incorporated in terms of exact, simply elegant, and absolutely terminating finite summed Lauricella functions which eliminate the secular divergence problem and pave way for a comprehensive understanding of certain exotic phenomena of various two-dimensional regular and irregular quantum dots. A simple yet highly accurate and exact variational wave function in terms of Whittaker-M function extensible to multiexcitonic systems has been propounded. We have also presented a formulation extending the size of the systems to triexcitonic (e-e-h/e-h-h), biexcitonic (e-h-e-h), and multiexcitonic ("N" e-h pair) planar dots by mono-, di-, quadru-, and octopole expansions. As a benchmark, we have examined the energy spectra, level-spacing statistics, heat capacities (C v at 1 K), and magnetization (T ≈ 0-1 K) of He/SiO2/BN/GaAs model systems for different lateral confinements, magnetic fields, mass ratios of e-h, and dielectric constants (ϵ).