Transient electrostatic deposition of particles from a monodisperse aerosol cloud moving past a perfectly conducting spherical collector is studied by means of direct numerical simulation. Two ideal cases of electrically grounded and insulated spheres are considered. In the case of a grounded sphere the Coulomb interaction between moving charged aerosol cloud and the induced electrical charges on the sphere causes significant enhancement of particle deposition. Important characteristics of the process, such as rates of deposition, the deposited mass, and typical cloud configurations for various values of dimensionless time and parameter of electrostatic interaction are found. It is shown that charging of the insulated target by arriving aerosol particles and electrostatic expansion of the cloud due to reciprocal repulsion of the charged particles can substantially impede the deposition process.