Script to Delete records in multiple table
You have to achieve this using Dynamic SQL Query

1- First you have to list all Tables With there Corresponding Databases in a Temp Table
2- Building Query for databases that contains Students and Winners dataTable

Your script should look like

--Get all Databases With corresponding Database

declare @SQL nvarchar(max)
DECLARE @strQuery AS NVARCHAR(MAX)

SET @strQuery = ''

CREATE TABLE #TblTemp (DatabaseName Varchar(255), Tablename Varchar(255))



set @SQL = (select 'union all 
select '''+D.name+''' as DatabaseName,
       T.name collate database_default as TableName
from '+quotename(D.name)+'.sys.tables as T
'
from sys.databases as D
for xml path(''), type).value('substring((./text())[1], 13)', 'nvarchar(max)')

--print @SQL
INSERT INTO #TblTemp
exec (@SQL)

-- Building Queries

SELECT @strQuery = @strQuery + 'Delete T1 from [' + name  + '].dbo.Students As T2
                        Inner join  [' + name  + '].dbo.Winners as T1 
                        On T1.[st_ID] = T2.[ID] 
                        Where    T1.[name] = IN(''Roy'',''Peter'')  ;

DELETE FROM [' + name  + '].dbo.Students WHERE [name] = IN(''Roy'',''Peter'') ;

'

 from sys.databases
 WHERE EXISTS (SELECT 1 FROM #TblTemp WHERE #TblTemp.DatabaseName = name AND #TblTemp.TableName = 'Students') AND
 EXISTS (SELECT 1 FROM #TblTemp WHERE #TblTemp.DatabaseName = name AND #TblTemp.TableName = 'Winners')

--VIEW QUERIES (you can copy result and execute it manually)
SELECT @strQuery



--EXECUTE QUERIES
EXEC(@strQuery)

--DROP Temp Table 
DROP TABLE #TblTemp


This Will Result a query like the following (If these databases contains Students and Winners Table)

Delete T1 from [master].dbo.Students As T2   Inner join  [master].dbo.Winners as T1    On T1.[st_ID] = T2.[ID]    Where    T1.[name] = IN('Roy','Peter')  ;     
DELETE FROM [master].dbo.Students WHERE [name] = IN('Roy','Peter') ;     
Delete T1 from [tempdb].dbo.Students As T2   Inner join  [tempdb].dbo.Winners as T1    On T1.[st_ID] = T2.[ID]    Where    T1.[name] = IN('Roy','Peter')  ;     
DELETE FROM [tempdb].dbo.Students WHERE [name] = IN('Roy','Peter') ;     
Delete T1 from [model].dbo.Students As T2   Inner join  [model].dbo.Winners as T1    On T1.[st_ID] = T2.[ID]    Where    T1.[name] = IN('Roy','Peter')  ;     
DELETE FROM [model].dbo.Students WHERE [name] = IN('Roy','Peter') ;     
Delete T1 from [msdb].dbo.Students As T2   Inner join  [msdb].dbo.Winners as T1    On T1.[st_ID] = T2.[ID]    Where    T1.[name] = IN('Roy','Peter')  ;     
DELETE FROM [msdb].dbo.Students WHERE [name] = IN('Roy','Peter') ;     
Delete T1 from [AdventureWorks2008R2].dbo.Students As T2   Inner join  [AdventureWorks2008R2].dbo.Winners as T1    On T1.[st_ID] = T2.[ID]    Where    T1.[name] = IN('Roy','Peter')  ;     DELETE FROM [AdventureWorks2008R2].dbo.Students WHERE [name] = IN('Roy','Peter') ;     Delete T1 from [DbMail].dbo.Students As T2   Inner join  [DbMail].dbo.Winners as T1    On T1.[st_ID] = T2.[ID]    Where    T1.[name] = IN('Roy','Peter')  ;     


I don't Now if that is what you was asking for in your question below (Your question was not specific like this one, so my answer was providing the dynamic sql logic in general)


Truncate with where clause