Q-M242 is the parent to all other Q branches. Its parent is P-M45. YFull dates show that Q-M242 is between 34,000 and 29,800 years old (95% CI). This is a much older date than in older published studies, and perhaps helps explain the great geographic spread of the branches under it.
I have long argued that Q is not a recent arrival in Europe. My belief has been supported by a new paper. The paper, The Genomic History Of Southeastern Europe, is in draft form at bioRxiv.