Need to scan all domain computers for .pst files

Question

I am new to powershell sctipting, like Brand new. I have some experience using Exchange powershell but thats always been for very specific items like adjust calendar permissions and such. Nothing to robust.
Currently I am working on a powershell script to push out via Group policy that will run aa search on each domain PC. I've been getting help from a co-worker but he isn't available right now and I have a hard time following him sometimes. I am this site and its user might be able to assist me. What I am trying to do(and I believe I am close to) is pulling a list of drives for each computer on the domain. Once I pull that list O pipe it into a variable and then do a search on that variable for any files that end with .pst. Once the search is complete if there were results from the search a file should be created with the FUllname"path" of each file and the computer name should be used for naming the file. If there are no results form the search the file would be empty but the filename should still be named after t he computer. I believe I have gotten everything correct except that I do not know how to name the file based on the computer name. Thank you for your time and help with this.
Here is my code so far:

$drives=Get-WmiObject -query "SELECT * from win32_logicaldisk where 
DriveType = '3'" | select deviceid
    foreach ($drive in $drives){
        $pstfound=Get-ChildItem $drive.deviceid *.pst -recurse | select 
        fullname
        $pst+=$pstfound
        }
        IF ($pst -eq $null) {
        $pst | Out-File \\"Servername"\Searchresults\Null
        } Else {
        $pst | Out-File \\"Servername"\Searchresults\HasItems
        }

Answer 1

Thank you. I wasn't initially planning on using the UNC path but changed it up anyways and I think that will make it easier to go through later. I also figured out my issue for naming the file generated after the computer it ran on. I just set a variable $hostname=hostname and then set the files as \\$hostname.csv