for what it's worth, I can give you a little simplification. The partitioning query doesn't have to be stated twice:

select acct.[Name], cont.fullname, cont.createdon

FROM [AccountBase] acct

JOIN (SELECT accountid, fullname, createdon

, ROW_NUMBER() OVER (PARTITION BY [AccountId]

ORDER BY createdon Desc) ROW_NUM

FROM [ContactBase]) cont

on cont.[AccountId] = acct.[AccountId]

where cont.ROW_NUM <= 3

order by acct.[Name], cont.fullname

You could have joined lvt directly to the sub query removing the middle level of nesting.

I'm betting this is vastly superior in performance to APPLY.