A braita cited authoritatively in the Talmud (Menachoth 40b-41a) seems to be pretty explicit that only a garment sufficient to cover a majority of a child is obligated in tzitzith:
טלית שהקטן מתכסה בו ראשו ורובו והגדול יוצא בה דרך עראי חייבת בציצית אין הקטן מתכסה בו ראשו ורובו אע"פ שהגדול יוצא בה עראי פטורה
A cloak with which a minor can cover his head and majority (of his body) and an adult would go out in it occasionally is obligated in tzitzith. If the minor can not cover his head and majority with it, even though an adult would occasionally go out in it, it is exempt.
Nonetheless, the Arokh HaShulchan (OC 16:5) attempts to defend a prevalent lenient practice regarding wearing small garments with tzitzit, even in reshut harabim (public domain) on Shabbath, which had previously been decried as a desecration of Shabbath, by arguing that any sized garment is obligated in tzitzith:
טלית קטן שתחת הבגדים אינה צריכה שיעור כלל, דאם רק יש בו ארבע כנפות – חייב בציצית
... A tallit katan worn under the clothes does not require any (minimum) measurement at all, for if it has four corners - it is obligated in tzitzith.
(See also op. cit. OC 8:4 and 10:20) Does this mean that the practice at the time was indeed to append tzitzith to every size of garment - e.g. scarves, neckties, etc? Wouldn't it be a tarti d'satri (contradiction) for a person to be wearing a small tallit simultaneously with - e.g. a scarf? Similarly, nowadays, if someone is wearing a less-than-shiur tallith katan (e.g. an adolescent), does that mean he must be relying on the Arokh HaShulchan and should not also wear a necktie?