Locate and copy from file

Consider the following:

Source directory with 5000 sub folders, each with hundreds of unique file names
Text file file with 1000 only unique file names - no path

I must copy only the files in the text file (remember no path) from the source while replicating the original path to a new destination drive

What would be an efficient method in powershell or DOS to read from the text file and copy the resulting files into a new source directory retaining the relative path in the destination?
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avatechAsked:
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becraigCommented:
$fpath = "F:"
$dest = "C:\destination"
gc .\files.txt | % {$named = $_;gci $fpath -recurse | ? {$_.name -eq $named } | % {$forig = $_.fullname;$nufile = $forig -replace $fpath, $dest;$nuname = ($_ | select -ExpandProperty DirectoryName) -replace $fpath, $dest ; if (!(Test-Path $nuname)) {New-Item -Path $nuname -ItemType Directory; "Directory created....."};Copy-Item $forig $nufile}}

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avatechAuthor Commented:
Testing this weekend it's been a low priority.
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