AD Migration from windows server 2003 to Windows server 2016

I'd check that domain functional level is at 2003 level. Also confirm health is 100% before trying.

I'd use dcdiag / repadmin tools to verify health correcting all errors found before starting. Then stand up the new 2016, patch it fully, license it, join existing domain, add active directory domain services, promote it also making it a GC (recommended), transfer FSMO roles over (optional), transfer pdc emulator role (optional), use dcdiag / repadmin tools to again verify health, when all is good you can decommission / demote old one.

If further assistance is needed then please run;

• Dcdiag /v /c /d /e /s:%computername% >c:\dcdiag.log
• repadmin /showrepl >C:\repl.txt
• ipconfig /all > C:\dc1.txt
• ipconfig /all > C:\dc2.txt
• (etc. as other exist)
  
  then put unzipped text files up on OneDrive and share a link.