The correct answer is A. My family tree is entitled The Smiths: One Hundred Years and Growing.
Explanation:
In grammar, the punctuation of a sentence mainly depends on the elements that compose it, in the case of the sentence "My family tree is entitled The Smiths One Hundred Years and Growing" this is a simple sentence which means this sentence is composed by a subject "My family tree", a verb "is entitled" and a complement "The Smiths One Hundred Years and Growing". Because of this, there is no need to place any punctuation mark between the subject, verb or complement as this would introduce unnecessary pauses and therefore is incorrect. However in the case of "The Smiths One Hundred Years and Growing" it is required to use a colon (:) after "The Smiths" considering in grammar the colon (:) is used to introduce an explanation, paraphrasing or a list of items related to a previous sentence, which is exactly the case of this sentence as "One Hundred Years and Growing" explains or paraphrase "The Smiths". Considering this, the sentence that is correctly punctuated is "A. My family tree is entitled The Smiths: One Hundred Years and Growing".