What is the purpose of those star like solder joints?
This patent from 2005 claims the idea (star shaped solder pads) and gives the motivation to be the desire to simplify the manufacturing process for boards that require both SMD and leaded components. Specifically, this seems to be a pad stencil optimization for the pin-in-paste*** reflow process for leaded components.
The SMD components are soldered with a paste and reflow process but the leaded components are traditionally done with a wave soldering process. The pin-in-paste process allows leaded components to be pasted and soldered together with the SMD components in a single reflow, eliminating the need for a second wave-soldering step.
When preparing a board for pin-in-paste the stencil needs to be enlarged - bigger than the solder pad - to accommodate enough paste as the leaded components require significantly more solder than SMD devices (since the solder wicks onto the lead and down into the through-hole). Other techniques are double-stamping the paste to force more of it down into the through-hole. The star pattern may just be a way to lay out the paste in an optimized way to shave down the total amount required, cutting costs.
The star shape may encourage the solder to pull under surface tension towards the lead and through-hole in the centre, allowing a thick stack of paste out to the points which largely is pulled towards the center, minimizing the spread after melting (a large circular pad would pull more solder out to the edge of the stencil, wasting material).
It's difficult to tell whether this board was soldered with paste and reflow or traditional wave, but if the former, this is one possibility.
It's also possible that these stars are there to augment the current carrying capacity of the pour layer underneath, particularly around vias and constrictions where the current density would otherwise become too high. This may afford the designers the ability to use a thinner copper layer (reducing costs) by adding these small enhancements in key locations where current concentrates.
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These are drainage shapes or solder thieves.
This patent shows something similar, as does the picture in this question. Maybe someone found the stars to work better during experiments, maybe someone just wanted to avoid the patent.
This is an area of the board where isolation matters, probably the power supply. There are even some spark gaps built using the available material (PCB traces) without additional cost, maybe underneath a common-mode choke, as they are often seen in the mains input filter (three pointy edges on opposite sides). These spark gaps do the exact opposite of the stars around the component pins: They are designed to increase the field when high voltage transients are present and the isolation gap is supposed to break down in a controlled fashion.
The stars' edges, on the contrary, do not point towards nearby traces or components.
When you look carefully, you can see how the stars' edges point towards wider areas of their own traces and not towards the designed clearance or creepage spacings or other traces. This is done to nudge the solder away from any isolation spacings.
When soldering through-hole components in what is called wave soldering, sometimes some solder will form edges or spikes when cooling off and becoming solid. To some extent, you may have noticed this effect even while hand soldering some joints. The keepouts in the green solder mask try to make the solder stick anywhere but in the designed isolations spacings.
I guess some clever process engineers have come up with this idea and have noticed how it can increase the yield - i.e. reduce the number of components that fail the visual inspection (or automated optical test) after the soldering process or even break down in the high-voltage isolation test that is done with the finished product, at least for the primary-to-secondary isolation (mains input to any low voltage circuits the user may touch).