Does this rainwater drainage configuration look right?

[grapefruitoclock]

The semi-detached house we've recently moved into has a gable and a dormer at the front. The rainwater drainage for both seems to empty out onto the tiles of the sloping roof to the left of the dormer, creating a stream. There is obvious wear and tear to the tiles in that location. Everywhere else on my house, the rainwater from the horizontal drainpipes flows into downpipes. Should there be a downpipe on the sloping roof? Or some other solution? I didn't notice a similar stream on my neighbour's roof, so not sure where her water is going.

My house is 20 years old and has something like this

I have a roof for the upper floor and then the bottom floor projects outwards and the lower roof is tiled.

So itt collects water off the upper roof into a gutter which then becomes a downpipe which decants the water onto the roof below. Like yours but the water runs down an open section of tiling rather than in a corner.

My corner has flashing to protect the join between the lower roof and the wall of the upper floor.

My concern with yours would be water ingress where the water runs next to the brickwork.

I would ask the neighbour about theirs. Lots of people ask stuff about our house or us about theirs, ie who did your new gutters?

Maybe it needs a solution like this? ...

No, a significant down pipe should never run onto tiles really as they aren't designed to cope with a deluge, it's like a reason coat will keep you dry but if someone gets at you with a hose you'll still get wet. It should run into a hopper if possible but I'm not sure of the practical solutions