You will need to deploy the following DLL (available here: C:\Windows\SysWOW64 ) with the Delphi application:
In all cases:
Easyco32.dll
Easyco32.fr (for French support of Easycom dialog boxes).
Eac32slf.dll
Eac32prc.dll
If you use Easycom Native Driver without BDE:
EasycomIdapi.dll
If you use Easycom IDAPI Driver with BDE:
Ace40032.dll
The BDE must be operational on PC where application is deployed.
For the deployment you can avoid the usage of the .ini file (this is recommended) and use the "DriverName" property of a TEacDatabase component.
You also might want to deploy the easycom ini file (EasycomAlias.ini and Easycom.ini).