Your macro is just splitting all the rows in the selected range, including the header row in the first row (so it will appear just one time, in the first file). I modified the macro for what you're asking; it's easy, review the comments I wrote to see what it does.
Sub Test()
Dim wb As Workbook
Dim ThisSheet As Worksheet
Dim NumOfColumns As Integer
Dim RangeToCopy As Range
Dim RangeOfHeader As Range 'data (range) of header row
Dim WorkbookCounter As Integer
Dim RowsInFile 'how many rows (incl. header) in new files?
Application.ScreenUpdating = False
'Initialize data
Set ThisSheet = ThisWorkbook.ActiveSheet
NumOfColumns = ThisSheet.UsedRange.Columns.Count
WorkbookCounter = 1
RowsInFile = 10 'as your example, just 10 rows per file
'Copy the data of the first row (header)
Set RangeOfHeader = ThisSheet.Range(ThisSheet.Cells(1, 1), ThisSheet.Cells(1, NumOfColumns))
For p = 2 To ThisSheet.UsedRange.Rows.Count Step RowsInFile - 1
Set wb = Workbooks.Add
'Paste the header row in new file
RangeOfHeader.Copy wb.Sheets(1).Range("A1")
'Paste the chunk of rows for this file
Set RangeToCopy = ThisSheet.Range(ThisSheet.Cells(p, 1), ThisSheet.Cells(p + RowsInFile - 2, NumOfColumns))
RangeToCopy.Copy wb.Sheets(1).Range("A2")
'Save the new workbook, and close it
wb.SaveAs ThisWorkbook.Path & "est" & WorkbookCounter
wb.Close
'Increment file counter
WorkbookCounter = WorkbookCounter + 1
Next p
Application.ScreenUpdating = True
Set wb = Nothing
End Sub
Hope this helps.
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