If you don't need to receive e-mail from other people by your smtp server, you don't need to register your domain.
If you only need to send e-mail, you can use your smtp server for your application server.
but you need to config your smtp server about authentication and relay for your application server.
about authentication, if your smtp server and application is difference machine, you config to allow the anonymous logon except your servers is in the same domain.
about relay, you config to allow the only your application server can relay to your smtp server.
after setting for authentication and relay, you write code by using cdo object for sending e-mail
as following, the sample asp code for sending e-mail by smtp server.
'Sending SMTP mail via port 25 using CDOSYS
'This ASP page uses CDOSYS to send SMTP mail using port 25 of the SMTP server that is set. The e-mail delivery is handled by the SMTP server that is set in the configuration object.
<%@ Language=VBScript %>
<META NAME="GENERATOR" Content="Microsoft Visual Studio 6.0">
' send by connecting to port 25 of the SMTP server
Const cdoSendUsingPort = 2
StrSmartHost = "mail.example.com"
set iMsg = CreateObject("CDO.Message")
set iConf = CreateObject("CDO.Configuration")
Set Flds = iConf.Fields
' set the CDOSYS configuration fields to use port 25 on the SMTP server
.Item("http://schemas.microsoft.com/cdo/configuration/sendusing") = cdoSendUsingPort
.Item("http://schemas.microsoft.com/cdo/configuration/smtpserver") = strSmartHost
.Item("http://schemas.microsoft.com/cdo/configuration/smtpconnectiontimeout") = 10
' build HTML for message body
strHTML = "<HTML>"
strHTML = strHTML & "<HEAD>"
strHTML = strHTML & "<BODY>"
strHTML = strHTML & "<b> This is the test HTML message body</b></br>"
strHTML = strHTML & "</BODY>"
strHTML = strHTML & "</HTML>"
' apply the settings to the message
Set .Configuration = iConf
.To = "email@example.com"
.From = "firstname.lastname@example.org"
.Subject = "This is a test CDOSYS message (Sent via Port 25)"
.HTMLBody = strHTML
' cleanup of variables
Set iMsg = Nothing
Set iConf = Nothing
Set Flds = Nothing
you can also use the asp.net code.
search about CDO object...