Finding a Top Level Parent in SQL

You can use recursive CTE to achieve that:

DECLARE @childID INT 
SET @childID  = 1 --chield to search

;WITH RCTE AS
(
    SELECT *, 1 AS Lvl FROM RelationHierarchy 
    WHERE ChildID = @childID

    UNION ALL

    SELECT rh.*, Lvl+1 AS Lvl FROM dbo.RelationHierarchy rh
    INNER JOIN RCTE rc ON rh.CHildId = rc.ParentId
)
SELECT TOP 1 id, Name
FROM RCTE r
inner JOIN dbo.Person p ON p.id = r.ParentId
ORDER BY lvl DESC

SQLFiddle DEMO

EDIT - for updated request for top level parents for all children:

;WITH RCTE AS
(
    SELECT  ParentId, ChildId, 1 AS Lvl FROM RelationHierarchy 

    UNION ALL

    SELECT rh.ParentId, rc.ChildId, Lvl+1 AS Lvl 
    FROM dbo.RelationHierarchy rh
    INNER JOIN RCTE rc ON rh.ChildId = rc.ParentId
)
,CTE_RN AS 
(
    SELECT *, ROW_NUMBER() OVER (PARTITION BY r.ChildID ORDER BY r.Lvl DESC) RN
    FROM RCTE r

)
SELECT r.ChildId, pc.Name AS ChildName, r.ParentId, pp.Name AS ParentName
FROM CTE_RN r
INNER JOIN dbo.Person pp ON pp.id = r.ParentId
INNER JOIN dbo.Person pc ON pc.id = r.ChildId
WHERE RN =1

SQLFiddle DEMO

EDIT2 - to get all persons change JOINS a bit at the end:

SELECT pc.Id AS ChildID, pc.Name AS ChildName, r.ParentId, pp.Name AS ParentName
FROM dbo.Person pc 
LEFT JOIN CTE_RN r ON pc.id = r.CHildId AND  RN =1
LEFT JOIN dbo.Person pp ON pp.id = r.ParentId

SQLFiddle DEMo

To find all top-level parents, use a query like:

select p.Name
from Person p
where not exists
(select null
 from RelationHierarchy r
 where r.ChildId = p.Id)

SQLFiddle here.

To find the top-level parent of a specific child, use:

with cte as
(select t.ParentId TopParent, t.ChildId 
 from RelationHierarchy t
 left join RelationHierarchy p on p.ChildId = t.ParentId
 where p.ChildId is null
 union all
 select t.TopParent TopParent, c.ChildId 
 from cte t
 join RelationHierarchy c on t.ChildId = c.ParentId)
select p.name
from cte h
join Person p on h.TopParent = p.Id
where h.ChildId=3 /*or whichever child is required*/

SQLFiddle here.

I've used this pattern to associate items in a hierarchy with the item's root node.

Essentially recursing the hierarchies maintaining the values of the root node as additional columns appended to each row. Hope this helps.

with allRows as (
    select ItemId, ItemName, ItemId [RootId],ItemName [RootName] 
    from parentChildTable
    where ParentItemId is null
    union all
    select a1.ItemId,a1.ItemName,a2.[RootId],a2.[RootName]
    from parentChildTable a1
    join allRows a2 on a2.ItemId = a1.ParentItemId
)   

select * from allRows

Try this.

The recursive CTE will find the person and walk up the hierarchy until it finds no parent.

-- This CTE will find the ancestors along with a measure of how far up
-- the hierarchy each ancestor is from the selected person.
with ancestor as (
  select ParentId as AncestorId, 0 as distance
  from RelationHierarchy
  where CHildId = ?

  union all

  select h.ParentId, a.distance + 1
  from ancestor a inner join RelationHierarchy rh on a.AncestorId = rh.ChildId
)
select AncestorId
from ancestor
where distance = (select max(distance) from ancestor)