The following is a primer on managing virtual hard drives using Hyper-V manager. Virtual hard disk files are stored as either .vhd or .vhdx files which use .avhd and .avhdx differencing disks respectively for snapshots. Both formats support either fixed size or dynamically expanding. The .vhdx format is new as of Server 2012 and provides some improvements over the previous .vhd format including increased storage capacity.
For a list of changes in the VHDX format, see http://technet.microsoft.com/en-us/library/hh831446.aspx
All examples are performed using Hyper-V 3.0 on Windows Server 2012 (minimum version required).