My TK Page:

Takeru Takaishi, (T.K): TK for short, is Matt's little brother. He doesn't live with Matt, which is why there's a tiny bit of friction between the two boys. But T.K. looks up to Matt, striving his hardest to make his big brother feel proud of him and to earn his respect, which isn't easy for the little guy. Matt thinks it's up to him to keep his little brother safe in this world, which can put too much pressure on a boy. T.K. was the youngest member of the group of kids that had fallen into Digiworld, before Kari arrived. Because he's so little, he often feels like he's just in bigger kids' way. He tries very hard to be brave even when bad and scary things happen. He's afraid that the others think he's nothing more than a crybaby. Kari is the only other Digi-Destined his age, and he cares for her as a special friend.

T.K. lives with his mom, and Matt lives with their dad, because their parents are divorced.
In the Digimon Movie we see TK's Gran who is crazy and always falls asleep on TK

T.K. and Patamon may seem sweet and innocent--and they are--but they also pull their share of the weight in the fight against evil in the Digiworld.

Season 2: T.K. has grown up a lot since he was a Digi-Destined as a little kid, and not just in stature. His voice has deepened too. He and his mom have moved to Tai and Kari's hometown, and he's now in seventh grade in the same class as Kari and Davis. He and Davis don't always get along.

25 years later:
TK is a novelist and he is working on a series of books about adventures in the Digital world. He has one son.