Append many imported files to a worksheet

In the modified code below I am trying to import text files (.OUT) and append each file by rows onto sheet 4.
What I get is each file plastered about the worksheet.
Some of the data is properly entered in columns "A thru H" and some of the files append rows within the same columns while others are placed in columns "I thru P" in the same rows and others are further out in the columns.

Option Explicit

'Bill Manville's modified code
Sub ImportFilesInFolder()
Dim aFiles() As String, iFile As Integer
Dim stFile As String, vFile As Variant
Dim stDirectory As String
Dim stCode As String
Dim sMyRange As String
Dim Sh4LastRow As String
Dim Sh4Range As Range

    ' first build an array of the files and then process them
    ' this is because you may upset the Dir function if you save a file

stDirectory = "C:\MEASURE-6000\OUTPUT\"  ' name of directory to look in
    ' use Dir function to find XLS files in Directory
    stFile = Dir(stDirectory & "*.OUT")
    If stFile = "" Then Exit Sub    ' no files to process
    Do While stFile <> ""
        ' add to array of files
        iFile = iFile + 1
        ' add one element to the array
        ReDim Preserve aFiles(1 To iFile)
        aFiles(iFile) = stFile
        stFile = Dir()   ' gets next file
    Loop
    'MsgBox iFile    ' for testing

    With Sheets("Sheet4")    'Loop thru Column C
        Sh4LastRow = .Cells(Rows.Count, "C").End(xlUp).Row
        Set Sh4Range = .Range("C1:C" & Sh4LastRow)

        If .Range("A1").Value = "" Then
            sMyRange = "A" & Sh4LastRow + 1
            'MsgBox sMyRange 'for testing
            ' process the files
            For Each vFile In aFiles
                'MsgBox stDirectory & "\" & vFile    'for testing, actual file name
                'Add data to worksheet and append each new _
                import in columns A thru H
                With .QueryTables.Add( _
                     Connection:="TEXT;" & stDirectory & vFile, _
                     Destination:=.Range(sMyRange))
                    .FieldNames = True
                    .RowNumbers = False
                    .FillAdjacentFormulas = False
                    .PreserveFormatting = True
                    .RefreshOnFileOpen = False
                    .RefreshStyle = xlInsertDeleteCells
                    .SavePassword = False
                    .SaveData = True
                    .AdjustColumnWidth = True
                    .RefreshPeriod = 0
                    .TextFilePromptOnRefresh = False
                    .TextFilePlatform = xlWindows
                    .TextFileStartRow = Sh4LastRow + 1
                    .TextFileParseType = xlDelimited
                    .TextFileTextQualifier = xlTextQualifierDoubleQuote
                    .TextFileConsecutiveDelimiter = True
                    .TextFileTabDelimiter = True
                    .TextFileSemicolonDelimiter = False
                    .TextFileCommaDelimiter = True
                    .TextFileSpaceDelimiter = True
                    .TextFileColumnDataTypes = Array(1, 1, 1, 1, 1, 1, 1, 1)
                    .Refresh BackgroundQuery:=False
                End With
            Next vFile
        End If
    End With
End Sub

Any hints, tips and or examples are appreciated.
See attached excel file of sheet 4.