Branches: A tree with a single trunk that sprouts forth multiple trunklets, none of which are (usually) as thick as the main single trunk. These trunklets are branches.
In mass-transit, a route can have a main trunk, but then splits into multiple trunklets or 'branches', none of which usually have the same frequency of service as the main trunk. For transit planners, this can be an easy solution in the paradigm of constrained budgets. For riders, it can be confusing and frustrating.
Once upon a time, METRO's current 82 Westheimer was a route with branches: Sharpstown, Woodlake, Dairy Ashford, and West Oaks. A few years ago, the 82's Sharpstown branch was renumbered as the 81 Westheimer Sharpstown, but for the longest time when we METRO riders looked for a bus on Westheimer, we had to make sure the 82 we were boarding was the correct one, lest we wind up at Eldridge when we meant to get off at Bellaire Boulevard!
Additionally, the 82 once upon a time also had said branch going into the Woodlake neighborhood near Westheimer @ Gessner, coming back down to Westheimer via Westerland, but that branch was done away with at least ten years ago. The 82 still has, interestingly enough, a Saturday-westbound-late-night truncation taking it as far as Dairy Ashford up to about 1:30am, though come System Reimagining's implementation, the Westheimer routing will take one all the way to West Oaks Mall and back with no truncations at all.
In the long history of bus route branching in Greater Houston, the history of Westheimer is tame. At one time, our METRO had the No. 10 Jensen with about eight branches, from which more than a few of today's routes are descended, and if my history is correct, the old 44 Studewood was the mother of many a current bus route.
And then, there is the current 40 Pecore / Telephone...
In System Reimagining, as far as I can tell, with one exception, there are no branches whatsoever - one of many earth-shattering revolutions in our coming new local bus system along with consistent spans of service across all seven days a week and every non-peak-only route running seven days a week, few deviations, and a greatly-expanded Frequent Network.
What we do have are what are called in METRO's lingo 'long lines' - routes with a high-frequency segment and a lower-frequency extension. An example is the new 6 Jensen / Greens, the high frequency segment of which starts at the Downtown TC and goes to the Tidwell TC. The 'long line' extends the route to Greenspoint TC with a base headway on this long line of one hour.
Routes in the new network with extensions are the 6 Jensen / Greens, 11 Almeda / Lyons, 20 Canal / Memorial, 44 Acres Homes, 49 Chimney Rock / S Post Oak, 54 Scott, 60 Cambridge, 80 MLK / Lockwood, 85 Antoine / Washington, and the 137 Northshore Flyer. A full description of all these routes in a .pdf form may be had HERE via the links found at the bottom of linked page.
The lone route in the Reimagined network with true branches turns out to be the 25 Richmond, which branches out from Wilcrest, one branch taking one all the way to Mission Bend Park & Ride and the other very small branch serving as a turnback for buses traveling the Frequent Network part of the route, taking in the Walnut Bend - Wilcrest - Westheimer terminus of the current 2 Bellaire Westchase branch.