Where necessary. If I can't offer a client the level of support they need, I'll give them the option of signing up with a trusted third party.
At some point on the future, this will probably become transparent. I work pretty closely with a number of other consultants and companies.
Not this particular part. Although I do have a reseller account ... so I guess you could say that I rely on a third party there.
But in this day and age, I don't know many services of any size that don't rely on external support.