In this note (R,m) denotes a complete regular local ring and B mostly denotes its absolute integral closure. The four objectives of this paper are the following: i) to determine the highest non-vanishing local cohomology of ΩB/R in equicharacteristic 0, ii) to establish a connection between each of ΩB/R and ΩB/V and pull-back of ΩA/V via a short exact sequence together with new observations on corresponding local cohomologies in mixed characteristic where V is the coefficient ring of R and A is its absolute integral closure, iii) to demonstrate that ΩB/R can be mapped onto a cohomologically Cohen-Macaulay module and iv) to study torsion-free property for ΩC/V and ΩC/k along with their respective completions where C is an integral domain and a module finite extension of R. In this connection an extension of Suzuki's theorem on normality of complete intersections to the formal set-up in all characteristics is accomplished.