We discuss a generalize Wagner number, a dimensionless system quantity that was applied recently as a tool to analyze the gross features of the morphology of quasi-two-dimensional electrodeposits. This generalized Wagner number incorporates the main processes involved in electrodeposition (charge transfer across the solid-liquid interface, ionic migration within the solution, and mass transport) and treats the LR potential drop across the cell. It is pertinent to the gross form of the deposit as well as to its texture and combines these different scales within a single theoretical framework. We present a general derivation, discuss several limiting cases, and suggest criteria for various morphological behaviors. We give explicit and simple expressions for a rectangular cell configuration, as an important example, discuss their validity, and illustrate the behavior with model calculations.